{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"2022-01-21-probability.ipynb","provenance":[{"file_id":"https://github.com/recohut/nbs/blob/main/raw/T125796%20%7C%20Probability%20Theory%20and%20the%20Sample%20Space%20Analysis.ipynb","timestamp":1644659150858}],"collapsed_sections":[],"authorship_tag":"ABX9TyP9Re9v/l/OlQ471mfP7hGJ"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","source":["# Probability Theory and the Sample Space Analysis"],"metadata":{"id":"jRc-QwQHUve-"}},{"cell_type":"markdown","metadata":{"id":"hquHcU8cZFob"},"source":["Few things in life are certain; most things are driven by chance. Whenever we cheer for our favorite sports team, or purchase a lottery ticket, or make an investment in the stock market, we hope for some particular outcome, but that outcome cannot ever be guaranteed. Randomness permeates our day-to-day experiences. Fortunately, that randomness can still be mitigated and controlled. We know that some unpredictable events occur more rarely than others and that certain decisions carry less uncertainty than other much-riskier choices. Driving to work in a car is safer than riding a motorcycle. Investing part of your savings in a retirement account is safer than betting it all on a single hand of blackjack. We can intrinsically sense these trade-offs in certainty because even the most unpredictable systems still show some predictable behaviors. These behaviors have been rigorously studied using *probability theory*. Probability theory is an inherently complex branch of math. However, aspects of the theory can be understood without knowing the mathematical underpinnings. In fact, difficult probability problems can be solved in Python without needing to know a single math equation. Such an equation-free approach to probability requires a baseline understanding of what mathematicians call a *sample space*.\n","\n","Certain actions have measurable outcomes. A *sample space* is the set of all the possible outcomes an action could produce. Let’s take the simple action of flipping a coin. The coin will land on either heads or tails. Thus, the coin flip will produce one of two measurable outcomes: *heads* or *tails*. By storing these outcomes in a Python set, we can create a sample space of coin flips."]},{"cell_type":"markdown","metadata":{"id":"RWImfNkJ3CHg"},"source":["## Unbiased Coin"]},{"cell_type":"code","metadata":{"id":"8Ji6E6MJ3GpR"},"source":["sample_space = {'Heads', 'Tails'}"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"KQ56sMsR3IIQ","executionInfo":{"status":"ok","timestamp":1637252642083,"user_tz":-330,"elapsed":476,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"cb491ed4-b197-4a2c-dc6a-a21651d9e441"},"source":["probability_heads = 1 / len(sample_space)\n","print(f\"Probability of choosing heads is {probability_heads}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability of choosing heads is 0.5\n"]}]},{"cell_type":"markdown","metadata":{"id":"chd76aZ43anP"},"source":["![image.png](data:image/png;base64,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)"]},{"cell_type":"markdown","metadata":{"id":"bMlY08hi3fIL"},"source":["*figure: Four event conditions applied to a sample space. The sample space contains two outcomes: heads and tails. Arrows represent the event conditions. Every event condition is a yes-or-no function. Each function filters out those outcomes that do not satisfy its terms. The remaining outcomes form an event. Each event contains a subset of the outcomes found in the sample space. Four events are possible: heads, tails, heads or tails, and neither heads nor tails.*"]},{"cell_type":"code","metadata":{"id":"mNlRBK_C3Kwf"},"source":["def is_heads_or_tails(outcome): return outcome in sample_space\n","def is_neither(outcome): return not is_heads_or_tails(outcome)\n","def is_heads(outcome): return outcome == \"Heads\"\n","def is_tails(outcome): return outcome == \"Tails\""],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"KIG-UCEe3v4A"},"source":["def get_event(event_condition, sample_space):\n","  return set([outcome for outcome in sample_space if event_condition(outcome)])"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"85zVHfi53nXt","executionInfo":{"status":"ok","timestamp":1637252869285,"user_tz":-330,"elapsed":468,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"4db3f15a-e701-47c1-bf80-85fae6bff039"},"source":["event_conditions = [is_heads_or_tails, is_heads, is_tails, is_neither]\n","\n","for event_condition in event_conditions:\n","    print(f\"Event Condition: {event_condition.__name__}\")\n","    event = get_event(event_condition, sample_space)\n","    print(f'Event: {event}\\n')"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Event Condition: is_heads_or_tails\n","Event: {'Heads', 'Tails'}\n","\n","Event Condition: is_heads\n","Event: {'Heads'}\n","\n","Event Condition: is_tails\n","Event: {'Tails'}\n","\n","Event Condition: is_neither\n","Event: set()\n","\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Hsf8Jqry36nH","executionInfo":{"status":"ok","timestamp":1637252918423,"user_tz":-330,"elapsed":692,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"671a2bbe-7ee8-4d5b-bbe3-a479d58983cf"},"source":["def compute_probability(event_condition, sample_space):\n","  event = get_event(event_condition, sample_space)\n","  return len(event) / len(sample_space)\n","\n","for event_condition in event_conditions:\n","    print(f\"Event Condition: {event_condition.__name__}\")\n","    probability = compute_probability(event_condition, sample_space)\n","    print(f'Probability: {probability}\\n')"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Event Condition: is_heads_or_tails\n","Probability: 1.0\n","\n","Event Condition: is_heads\n","Probability: 0.5\n","\n","Event Condition: is_tails\n","Probability: 0.5\n","\n","Event Condition: is_neither\n","Probability: 0.0\n","\n"]}]},{"cell_type":"markdown","metadata":{"id":"MVD3YMdg33Hc"},"source":["## Biased Coin"]},{"cell_type":"code","metadata":{"id":"FVYk7dcQ4Q-x"},"source":["weighted_sample_space = {'Heads': 4, 'Tails': 1}"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"eVJ7zsBr4WH1"},"source":["sample_space_size = sum(weighted_sample_space.values())\n","assert sample_space_size == 5"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"JsBW__Fn4pkY"},"source":["# Checking the weighted event size\n","\n","event = get_event(is_heads_or_tails, weighted_sample_space)\n","event_size = sum(weighted_sample_space[outcome] for outcome in event)\n","assert event_size == 5"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"id":"tFc4NPEJ4qAc"},"source":["def compute_event_probability(event_condition, generic_sample_space):\n","  event = get_event(event_condition, generic_sample_space)\n","  if type(generic_sample_space) == type(set()):\n","    return len(event) / len(generic_sample_space)\n","  event_size = sum(generic_sample_space[outcome] for outcome in event)\n","  return event_size / sum(generic_sample_space.values())"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"S1Kg34eM4_Yo","executionInfo":{"status":"ok","timestamp":1637253131780,"user_tz":-330,"elapsed":481,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"8409d865-6ed3-4710-c50c-50a127347e4a"},"source":["for event_condition in event_conditions:\n","    prob = compute_event_probability(event_condition, weighted_sample_space)\n","    name = event_condition.__name__\n","    print(f\"Probability of event arising from '{name}' is {prob}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability of event arising from 'is_heads_or_tails' is 1.0\n","Probability of event arising from 'is_heads' is 0.8\n","Probability of event arising from 'is_tails' is 0.2\n","Probability of event arising from 'is_neither' is 0.0\n"]}]},{"cell_type":"markdown","metadata":{"id":"INX2w3X35CiQ"},"source":["## Analyzing a family with four children"]},{"cell_type":"markdown","metadata":{"id":"6cCseJUb5RdR"},"source":["Suppose a family has four children. What is the probability that exactly two of the children are boys? We’ll assume that each child is equally likely to be either a boy or a girl. Thus we can construct an unweighted sample space where each outcome represents one possible sequence of four children, as shown in figure below:"]},{"cell_type":"markdown","metadata":{"id":"W83_D_Gh5UeE"},"source":["![image.png](data:image/png;base64,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)"]},{"cell_type":"markdown","metadata":{"id":"4l6hbOVb5TN8"},"source":["*fgiure: The sample space for four sibling children. Each row in the sample space contains 1 of 16 possible outcomes. Every outcome represents a unique combination of four children. The sex of each child is indicated by a letter: B for boy and G for girl. Outcomes with two boys are marked by an arrow. There are six such arrows; thus, the probability of two boys equals 6 / 16.*"]},{"cell_type":"code","metadata":{"id":"AmXqH2Au5ZQG"},"source":["from itertools import product\n","\n","possible_children = ['Boy', 'Girl']\n","\n","# Naive approach\n","sample_space = set()\n","for child1 in possible_children:\n","    for child2 in possible_children:\n","        for child3 in possible_children:\n","            for child4 in possible_children:\n","                outcome = (child1, child2, child3, child4)\n","                sample_space.add(outcome)\n","\n","# Better approach\n","all_combinations = product(*(4 * [possible_children]))\n","assert set(all_combinations) == sample_space\n","\n","# Best approach\n","sample_space_efficient = set(product(possible_children, repeat=4))\n","assert sample_space == sample_space_efficient"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"pmjwZCXI9afU","executionInfo":{"status":"ok","timestamp":1637254279656,"user_tz":-330,"elapsed":508,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"50ef59ce-94e0-4c8b-cbe3-e0105bbccf74"},"source":["sample_space"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["{('Boy', 'Boy', 'Boy', 'Boy'),\n"," ('Boy', 'Boy', 'Boy', 'Girl'),\n"," ('Boy', 'Boy', 'Girl', 'Boy'),\n"," ('Boy', 'Boy', 'Girl', 'Girl'),\n"," ('Boy', 'Girl', 'Boy', 'Boy'),\n"," ('Boy', 'Girl', 'Boy', 'Girl'),\n"," ('Boy', 'Girl', 'Girl', 'Boy'),\n"," ('Boy', 'Girl', 'Girl', 'Girl'),\n"," ('Girl', 'Boy', 'Boy', 'Boy'),\n"," ('Girl', 'Boy', 'Boy', 'Girl'),\n"," ('Girl', 'Boy', 'Girl', 'Boy'),\n"," ('Girl', 'Boy', 'Girl', 'Girl'),\n"," ('Girl', 'Girl', 'Boy', 'Boy'),\n"," ('Girl', 'Girl', 'Boy', 'Girl'),\n"," ('Girl', 'Girl', 'Girl', 'Boy'),\n"," ('Girl', 'Girl', 'Girl', 'Girl')}"]},"metadata":{},"execution_count":27}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"byz_MDHp5r8V","executionInfo":{"status":"ok","timestamp":1637253340652,"user_tz":-330,"elapsed":493,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"b3e3da91-3d54-4908-fd1d-5ff7754e0a00"},"source":["def has_two_boys(outcome): \n","  num = len([child for child in outcome if child == 'Boy']) == 2\n","  return num\n","\n","prob = compute_probability(has_two_boys, sample_space)\n","print(f\"Probability of 2 boys: {prob}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability of 2 boys: 0.375\n"]}]},{"cell_type":"markdown","metadata":{"id":"NsCBdutI54rD"},"source":["## Analyzing multiple die rolls"]},{"cell_type":"markdown","metadata":{"id":"ZUoZ5eDW55P8"},"source":["Suppose we’re shown a fair six-sided dice whose faces are numbered from 1 to 6. The die is rolled six times. What is the probability that these six die rolls add up to 21?\n","\n","We begin by defining the possible values of any single roll. These are integers that range from 1 to 6."]},{"cell_type":"code","metadata":{"id":"o663SyNI6TkQ"},"source":["numbers_on_die = list(range(1,7))\n","\n","sample_space_die = set(product(numbers_on_die, repeat=6))"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"MKEbMIvy5--6","executionInfo":{"status":"ok","timestamp":1637253435527,"user_tz":-330,"elapsed":502,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"43e12359-dd00-499b-c176-916819d17284"},"source":["def add_up_to_21(outcome):\n","  return sum(outcome) == 21\n","\n","prob = compute_event_probability(add_up_to_21, sample_space_die)\n","print(f\"Probability that a dice-roll out of 6 dice rolls add up to 21: {prob:2f}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability that a dice-roll out of 6 dice rolls add up to 21: 0.092850\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"njOXhlop6Mtw","executionInfo":{"status":"ok","timestamp":1637253467730,"user_tz":-330,"elapsed":10,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"febf923a-6335-4d68-dee6-1fa4c256c0c9"},"source":["prob = compute_event_probability(lambda x: sum(x) == 21, sample_space_die)\n","print(f\"Probability that a dice-roll out of 6 dice rolls add up to 21: {prob:2f}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability that a dice-roll out of 6 dice rolls add up to 21: 0.092850\n"]}]},{"cell_type":"markdown","metadata":{"id":"eyxakyPT6evS"},"source":["## Computing die-roll probabilities using weighted sample spaces\n","\n","We’ve just computed the likelihood of six die rolls summing to 21. Now, let’s recompute that probability using a weighted sample space. We need to convert our unweighted sample space set into a weighted sample space dictionary; this will require us to identify all possible die-roll sums. Then we must count the number of times each sum appears across all possible die-roll combinations. These combinations are already stored in our computed sample_space set. By mapping the die-roll sums to their occurrence counts, we will produce a weighted_sample_space result."]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"2H4_mqIi6k5C","executionInfo":{"status":"ok","timestamp":1637253558941,"user_tz":-330,"elapsed":567,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"2146fc83-5bd9-40a0-c7ec-88c90e753e34"},"source":["from collections import defaultdict\n","\n","weighted_sample_space = defaultdict(int)\n","\n","for outcome in sample_space_die:\n","  total = sum(outcome)\n","  weighted_sample_space[total] += 1\n","\n","weighted_sample_space"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["defaultdict(int,\n","            {6: 1,\n","             7: 6,\n","             8: 21,\n","             9: 56,\n","             10: 126,\n","             11: 252,\n","             12: 456,\n","             13: 756,\n","             14: 1161,\n","             15: 1666,\n","             16: 2247,\n","             17: 2856,\n","             18: 3431,\n","             19: 3906,\n","             20: 4221,\n","             21: 4332,\n","             22: 4221,\n","             23: 3906,\n","             24: 3431,\n","             25: 2856,\n","             26: 2247,\n","             27: 1666,\n","             28: 1161,\n","             29: 756,\n","             30: 456,\n","             31: 252,\n","             32: 126,\n","             33: 56,\n","             34: 21,\n","             35: 6,\n","             36: 1})"]},"metadata":{},"execution_count":19}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"CXy9hjvm6qxs","executionInfo":{"status":"ok","timestamp":1637253636155,"user_tz":-330,"elapsed":513,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"dd0f23dc-5d10-42bb-d35a-1795cd15b4eb"},"source":["num_combinations = weighted_sample_space.get(21)\n","print(f\"There are {num_combinations } ways for six rolled dice to sum to 21\")\n","\n","prob = compute_event_probability(lambda x: x == 21, weighted_sample_space)\n","print(f\"Probability that a dice-roll out of 6 dice rolls add up to 21: {prob:2f}\")\n","\n","print('Number of Elements in Unweighted Sample Space:')\n","print(len(sample_space_die))\n","\n","print('Number of Elements in Weighted Sample Space:')\n","print(len(weighted_sample_space))"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["There are 4332 ways for six rolled dice to sum to 21\n","Probability that a dice-roll out of 6 dice rolls add up to 21: 0.092850\n","Number of Elements in Unweighted Sample Space:\n","46656\n","Number of Elements in Weighted Sample Space:\n","31\n"]}]},{"cell_type":"markdown","metadata":{"id":"nQsE23eC69tJ"},"source":["## Computing probabilities over interval ranges"]},{"cell_type":"markdown","metadata":{"id":"tk21A6Bv7cy4"},"source":["So far, we’ve only analyzed event conditions that satisfy some single value. Now we’ll analyze event conditions that span intervals of values. An interval is the set of all the numbers between and including two boundary cutoffs. Let’s define an is_in_interval function that checks whether a number falls within a specified interval. We’ll control the interval boundaries by passing a minimum and a maximum parameter."]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"nWxbs-Zm7zb8","executionInfo":{"status":"ok","timestamp":1637253880332,"user_tz":-330,"elapsed":456,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"b003d388-6579-4d22-d7d0-bb24fa3a4b5e"},"source":["def is_in_interval(number, minimum, maximum):\n","  return minimum <= number <= maximum\n","  \n","prob = compute_event_probability(lambda x: is_in_interval(x, 10,21), weighted_sample_space)\n","print(f\"Probability of the interval: {prob:2f}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability of the interval: 0.544624\n"]}]},{"cell_type":"markdown","metadata":{"id":"T1k4o_AT75Ua"},"source":["Interval analysis is critical to solving a whole class of very important problems in probability and statistics. One such problem involves the evaluation of extremes, the problem boils down to whether obeserved data is too extreme to be believable. Data seems extreme when it is too unusual to have occurred by random chance. For instance, suppose we observe 10 flips of an allegedly fair coin, and that coin lands on heads 8 out of 10 times. Now, we had expected the coin to hit tails half the time, not 20% of the time, so the observations seem a little strange. Is the coin actually fair? Or has it been secretly replaced with a trick coin that falls on heads a majority of the time? We’ll try to find out by asking the following question: what is the probability that 10 fair coin-flips lead to an extreme number of heads? We’ll define an extreme head-count as observing of 8 heads or more. Thus, we can describe the problem as follows: what is the probability that 10 fair coin-flips produce between 8 and 10 heads?"]},{"cell_type":"code","metadata":{"id":"3HuRdIIT8GPj"},"source":["coin_sides = ['Heads', 'Tails']"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"pc2pkoil8H-6","executionInfo":{"status":"ok","timestamp":1637254025688,"user_tz":-330,"elapsed":622,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"14c419fe-d4d1-4368-cade-12402d4063ca"},"source":["from pprint import pprint\n","\n","def generate_coin_sample_space(num_flips):\n","  weighted_sample_space_coins = defaultdict(int)\n","  combinations = set(product(coin_sides, repeat=num_flips))\n","  for combination in combinations:\n","    num_heads = len([combo for combo in combination if combo == \"Heads\"])\n","    weighted_sample_space_coins[num_heads] += 1\n","  return weighted_sample_space_coins\n","  \n","weighted_sample_space_coins = generate_coin_sample_space(10)\n","pprint(weighted_sample_space_coins)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["defaultdict(<class 'int'>,\n","            {0: 1,\n","             1: 10,\n","             2: 45,\n","             3: 120,\n","             4: 210,\n","             5: 252,\n","             6: 210,\n","             7: 120,\n","             8: 45,\n","             9: 10,\n","             10: 1})\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"kQldhwmo8cwk","executionInfo":{"status":"ok","timestamp":1637254113254,"user_tz":-330,"elapsed":601,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"f019cd79-be5b-460d-f733-b1f684d3d17e"},"source":["prob = compute_event_probability(lambda x: is_in_interval(x, 8,10), weighted_sample_space_coins)\n","print(f\"Probability of observing more than 7 heads is {prob}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability of observing more than 7 heads is 0.0546875\n"]}]},{"cell_type":"markdown","metadata":{"id":"PSGMmS6Y8yKH"},"source":["Our observed head-count does not commonly occur. Does this mean the coin is biased? Not necessarily. Observing 8 out of 10 tails is as extreme as observing 8 out of 10 heads. Had we observed 8 tails and not 8 heads, we would still be suspicious of the coin. Our computed interval did not take this tails-driven extreme into account. Instead, we treated 8 or more tails as just another normal possibility. If we truly wish to measure the fairness of our coin, we’ll need to update our interval computations. We’ll need to include the likelihood of observing 8 or more tails. This is equivalent to observing 2 heads or less. Let's formulate the problem as follows; what is the probability that 10 fair coin-flips produce either 0 to 2 heads or 8 to 10 heads? Or, stated more concisely, what is the probability that the coin-flips do NOT produce between 3 and 7 heads?"]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"J12L7Zkv881T","executionInfo":{"status":"ok","timestamp":1637254163222,"user_tz":-330,"elapsed":624,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"8f257f61-8817-491d-f94a-43b1ed36686c"},"source":["prob = compute_event_probability(lambda x: not is_in_interval(x, 3, 7), weighted_sample_space_coins)\n","print(f\"Probability of observing more than 7 heads or 7 tails is {prob}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability of observing more than 7 heads or 7 tails is 0.109375\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"IyCtMAuI8-U2","executionInfo":{"status":"ok","timestamp":1637254175440,"user_tz":-330,"elapsed":3704,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"dc3ffbe1-624d-458b-876c-19c7a108bd46"},"source":["weighted_sample_space_20_flips = generate_coin_sample_space(20)\n","prob = compute_event_probability(lambda x: not is_in_interval(x, 5, 15),\n","                                 weighted_sample_space_20_flips)\n","print(f\"Probability of observing more than 15 heads or 15 tails is {prob}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability of observing more than 15 heads or 15 tails is 0.01181793212890625\n"]}]},{"cell_type":"markdown","metadata":{"id":"RtTYxjWi9AmB"},"source":["The updated probability has dropped from approximately .1 to approximately .01. Thus, the added evidence has caused a 10-fold decrease in our confidence of fairness.\n","\n","Despite this probability drop, the ratio of heads to tails has remained constant at 4-to-1. Both our original and updated experiments produced 80% heads and 20% tails. This leads to an interesting question: why does the probability of observing 80% or more heads decrease as the supposedly fair coin gets flipped more times?\n","\n","We can find out through detailed mathematical analysis. However, a much more intuitive solution is to just visualize the distribution of head-counts across our 2 sample space dictionaries. The visualization would effectively be a plot of keys (head-counts) vs values (combination counts) present in each dictionary."]},{"cell_type":"markdown","metadata":{"id":"gdHx9UEG9y_V"},"source":["## Plotting coin-flip probabilities"]},{"cell_type":"code","metadata":{"id":"cudqQ7Q8950d"},"source":["%matplotlib inline\n","\n","import matplotlib.pyplot as plt"],"execution_count":null,"outputs":[]},{"cell_type":"markdown","metadata":{"id":"1fLRPI7t9zdL"},"source":["We now have tools to visualize the relationship between a coin-flip count and the probability of heads. In section 1, we examined the probability of seeing 80% or more heads across a series of coin flips. That probability decreased as the coin-flip count went up, and we wanted to know why. We’ll soon find out by plotting head counts versus their associated coin-flip combination counts. These values were already computed in our section 1 analysis. The keys in the weighted_sample_space dictionary contain all possible head counts across 10 flipped coins. These head counts map to combination counts. Meanwhile, the weighted_sample_space_20_flips dictionary contains the head-count mappings for 20 flipped coins.\n","\n","Our aim is to compare the plotted data from both these dictionaries. We begin by plotting the elements of weighted_sample_space: we plot its keys on the x-axis versus the associated values on the y-axis. The x-axis corresponds to 'Head-count', and the y-axis corresponds to 'Number of coin-flip combinations with x heads'. We use a scatter plot to visualize key-to-value relationships directly without connecting any plotted points."]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"UbCBkyfT-vrs","executionInfo":{"status":"ok","timestamp":1637254677489,"user_tz":-330,"elapsed":12,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"4e6a971d-f478-4f90-bdf8-64dec982d31c"},"source":["def generate_coin_sample_space(num_flips=10):\n","    weighted_sample_space = defaultdict(int)\n","    for coin_flips in product(['Heads', 'Tails'], repeat=num_flips):\n","        heads_count = len([outcome for outcome in coin_flips\n","                          if outcome == 'Heads'])\n","        weighted_sample_space[heads_count] += 1\n","\n","    return weighted_sample_space\n","\n","weighted_sample_space = generate_coin_sample_space()\n","weighted_sample_space"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["defaultdict(int,\n","            {0: 1,\n","             1: 10,\n","             2: 45,\n","             3: 120,\n","             4: 210,\n","             5: 252,\n","             6: 210,\n","             7: 120,\n","             8: 45,\n","             9: 10,\n","             10: 1})"]},"metadata":{},"execution_count":36}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":287},"id":"tyQl5rbm94C5","executionInfo":{"status":"ok","timestamp":1637254682099,"user_tz":-330,"elapsed":624,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"502e0fd4-13d7-46b2-87c0-79cba1619883"},"source":["x_10_flips = list(weighted_sample_space.keys())\n","y_10_flips = [weighted_sample_space[key] for key in x_10_flips]\n","plt.scatter(x_10_flips, y_10_flips)\n","plt.xlabel('Head-count')\n","plt.ylabel('Number of coin-flip combinations with x heads')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"WM9mwWAG9-V9","executionInfo":{"status":"ok","timestamp":1637254687376,"user_tz":-330,"elapsed":785,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"d591522f-e3c5-4539-dce6-7c16c8a97490"},"source":["sample_space_size = sum(weighted_sample_space.values())\n","prob_x_10_flips = [value / sample_space_size for value in y_10_flips]\n","plt.scatter(x_10_flips, prob_x_10_flips)\n","plt.xlabel('Head-count')\n","plt.ylabel('Probability')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"id":"41rmTnxL-bs-"},"source":["assert sum(prob_x_10_flips) == 1.0"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"xrLfcsVA-Rij","executionInfo":{"status":"ok","timestamp":1637254706752,"user_tz":-330,"elapsed":547,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"88026bef-ea3b-4239-ba27-0a090ece840c"},"source":["plt.plot(x_10_flips, prob_x_10_flips)\n","plt.scatter(x_10_flips, prob_x_10_flips)\n","where = [is_in_interval(value, 8, 10) for value in x_10_flips]\n","plt.fill_between(x_10_flips, prob_x_10_flips, where=where)\n","plt.xlabel('Head-count')\n","plt.ylabel('Probability')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"AJIuRt1j-W_g","executionInfo":{"status":"ok","timestamp":1637254722955,"user_tz":-330,"elapsed":895,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"d49ba578-2eab-4f85-b077-a46c010acd3c"},"source":["plt.plot(x_10_flips, prob_x_10_flips)\n","plt.scatter(x_10_flips, prob_x_10_flips)\n","where = [not is_in_interval(value, 3, 7) for value in x_10_flips]\n","plt.fill_between(x_10_flips, prob_x_10_flips, where=where)\n","plt.xlabel('Head-count')\n","plt.ylabel('Probability')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"M-8MvksI_UVh","executionInfo":{"status":"ok","timestamp":1637254784981,"user_tz":-330,"elapsed":2299,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"42d54677-afd2-45e7-d2e1-5d7d9335e2f8"},"source":["weighted_sample_space_20_flips = generate_coin_sample_space(num_flips=20)\n","weighted_sample_space_20_flips"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["defaultdict(int,\n","            {0: 1,\n","             1: 20,\n","             2: 190,\n","             3: 1140,\n","             4: 4845,\n","             5: 15504,\n","             6: 38760,\n","             7: 77520,\n","             8: 125970,\n","             9: 167960,\n","             10: 184756,\n","             11: 167960,\n","             12: 125970,\n","             13: 77520,\n","             14: 38760,\n","             15: 15504,\n","             16: 4845,\n","             17: 1140,\n","             18: 190,\n","             19: 20,\n","             20: 1})"]},"metadata":{},"execution_count":44}]},{"cell_type":"code","metadata":{"id":"mADs29av_KIZ"},"source":["x_20_flips = list(weighted_sample_space_20_flips.keys())\n","y_20_flips = [weighted_sample_space_20_flips[key] for key in x_20_flips]\n","sample_space_size = sum(weighted_sample_space_20_flips.values())\n","prob_x_20_flips = [value / sample_space_size for value in y_20_flips]"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"Hss8PqrQ_MTa","executionInfo":{"status":"ok","timestamp":1637254786674,"user_tz":-330,"elapsed":1143,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"08a94c00-28d8-4947-a82c-cbe155996494"},"source":["plt.plot(x_10_flips, prob_x_10_flips)\n","plt.scatter(x_10_flips, prob_x_10_flips)\n","plt.plot(x_20_flips, prob_x_20_flips, color='black', linestyle='--')\n","plt.scatter(x_20_flips, prob_x_20_flips, color='k', marker='x')\n","plt.xlabel('Head-count')\n","plt.ylabel('Probability')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"gEmydVWx_O7p","executionInfo":{"status":"ok","timestamp":1637254792136,"user_tz":-330,"elapsed":774,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"3f876f57-a252-4c40-aa60-fd48cc6a2647"},"source":["plt.plot(x_10_flips, prob_x_10_flips, label='A: 10 coin-flips')\n","plt.plot(x_20_flips, prob_x_20_flips, color='k', linestyle='--',\n","         label='B: 20 coin-flips')\n","plt.legend()\n","\n","where_10 = [not is_in_interval(value, 3, 7) for value in x_10_flips]\n","plt.fill_between(x_10_flips, prob_x_10_flips, where=where_10)\n","where_20 = [not is_in_interval(value, 5, 15) for value in x_20_flips]\n","plt.fill_between(x_20_flips, prob_x_20_flips, where=where_20)\n","\n","plt.xlabel('Head-Count')\n","plt.ylabel('Probability')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"2d9JWNHn_dWd","executionInfo":{"status":"ok","timestamp":1637254816046,"user_tz":-330,"elapsed":927,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"af3cd21d-45d9-4bd8-cab8-e3f127091a76"},"source":["x_10_frequencies = [head_count /10 for head_count in x_10_flips]\n","x_20_frequencies = [head_count /20 for head_count in x_20_flips]\n","\n","plt.plot(x_10_frequencies, prob_x_10_flips, label='A: 10 coin-flips')\n","plt.plot(x_20_frequencies, prob_x_20_flips, color='k', linestyle=':', label='B: 20 coin-flips')\n","plt.legend()\n","\n","plt.xlabel('Head-Frequency')\n","plt.ylabel('Probability')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"XN4brxoN_fug","executionInfo":{"status":"ok","timestamp":1637254827793,"user_tz":-330,"elapsed":613,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"03a2e123-8cc2-4534-bd4d-faae41fc66b5"},"source":["relative_likelihood_10 = [10 * prob for prob in prob_x_10_flips]\n","relative_likelihood_20 = [20 * prob for prob in prob_x_20_flips]\n","\n","plt.plot(x_10_frequencies, relative_likelihood_10, label='A: 10 coin-flips')\n","plt.plot(x_20_frequencies, relative_likelihood_20, color='k',\n","         linestyle=':', label='B: 20 coin-flips')\n","\n","plt.fill_between(x_10_frequencies, relative_likelihood_10, where=where_10)\n","plt.fill_between(x_20_frequencies, relative_likelihood_20, where=where_20)\n","\n","plt.legend()\n","plt.xlabel('Head-Frequency')\n","plt.ylabel('Relative Likelihood')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"HvGTADSl_fqt"},"source":["## Simulating random coin flips and dice rolls using NumPy"]},{"cell_type":"code","metadata":{"id":"bFZpJUWPCUhV"},"source":["import numpy as np"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"n9EmrjOMCVan","executionInfo":{"status":"ok","timestamp":1637255582428,"user_tz":-330,"elapsed":679,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"d87beb7e-6dac-4a13-b604-5a566f242d70"},"source":["dice_roll = np.random.randint(1, 7)\n","assert 1 <= dice_roll <= 6\n","dice_roll"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["1"]},"metadata":{},"execution_count":51}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"9o9139MFCVXN","executionInfo":{"status":"ok","timestamp":1637255613688,"user_tz":-330,"elapsed":619,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"b81af27b-c4a0-450e-8cee-c296df88a2b9"},"source":["np.random.seed(0)\n","coin_flip = np.random.randint(0, 2)\n","print(f\"Coin landed on {'heads' if coin_flip == 1 else 'tails'}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Coin landed on tails\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"qL54HXrNCVUW","executionInfo":{"status":"ok","timestamp":1637255671409,"user_tz":-330,"elapsed":1023,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"9e36ed32-1a2b-4015-ff0a-a3060fe1eff5"},"source":["np.random.seed(0)\n","def frequency_heads(coin_flip_sequence):\n","    total_heads = sum(coin_flip_sequence)\n","    return total_heads / len(coin_flip_sequence)\n","\n","coin_flips = [np.random.randint(0, 2) for _ in range(10)]\n","freq_heads = frequency_heads(coin_flips)\n","print(f\"Frequency of Heads is {freq_heads}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Frequency of Heads is 0.8\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"mnG9ESg5CVRQ","executionInfo":{"status":"ok","timestamp":1637255692933,"user_tz":-330,"elapsed":628,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"7010678f-88b2-4d5d-d0e8-9128ec5889b5"},"source":["np.random.seed(0)\n","coin_flips = []\n","frequencies = []\n","for _ in range(1000):\n","    coin_flips.append(np.random.randint(0, 2))\n","    frequencies.append(frequency_heads(coin_flips))\n","\n","plt.plot(list(range(1000)), frequencies)\n","plt.axhline(.5, color='k')\n","plt.xlabel('Number of Coin Flips')\n","plt.ylabel('Head-Frequency')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"UgttiKvMCx0g","executionInfo":{"status":"ok","timestamp":1637255709206,"user_tz":-330,"elapsed":720,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"190cd253-ac2b-42ca-9fa2-c3ad88e22f3a"},"source":["np.random.seed(0)\n","print(\"Lets flip the biased coin once.\")\n","coin_flip = np.random.binomial(1, .7)\n","print(f\"Biased coin landed on {'heads' if coin_flip == 1 else 'tails'}.\")\n","\n","print(\"\\nLets flip the biased coin 10 times.\")\n","number_coin_flips = 10\n","head_count = np.random.binomial(number_coin_flips, .7)\n","print((f\"{head_count} heads were observed out of \"\n","       f\"{number_coin_flips} biased coin flips\"))"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Lets flip the biased coin once.\n","Biased coin landed on heads.\n","\n","Lets flip the biased coin 10 times.\n","6 heads were observed out of 10 biased coin flips\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"bsBTPiSbCxxC","executionInfo":{"status":"ok","timestamp":1637255720050,"user_tz":-330,"elapsed":781,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"063bc4b3-f98a-4d86-988c-14d2d8303d34"},"source":["np.random.seed(0)\n","head_count = np.random.binomial(1000, .7)\n","frequency = head_count / 1000\n","print(f\"Frequency of Heads is {frequency}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Frequency of Heads is 0.697\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"mlSS7HSrCxtE","executionInfo":{"status":"ok","timestamp":1637255749139,"user_tz":-330,"elapsed":523,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"32f2bed2-5700-48d4-ee0d-7049b0642937"},"source":["np.random.seed(0)\n","for i in range(1, 6):\n","    head_count = np.random.binomial(1000, .7)\n","    frequency = head_count / 1000\n","    print(f\"Frequency at iteration {i} is {frequency}\")\n","    if frequency == 0.7:\n","        print(\"Frequency equals the probability!\\n\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Frequency at iteration 1 is 0.697\n","Frequency at iteration 2 is 0.69\n","Frequency at iteration 3 is 0.7\n","Frequency equals the probability!\n","\n","Frequency at iteration 4 is 0.707\n","Frequency at iteration 5 is 0.702\n"]}]},{"cell_type":"markdown","metadata":{"id":"mRmPYNaq_fnb"},"source":["## Computing confidence intervals using histograms and NumPy arrays"]},{"cell_type":"markdown","metadata":{"id":"vOuUIkGZDOi9"},"source":["Suppose we’re handed a biased coin whose bias we don’t know. We flip the coin 1,000 times and observe a frequency of 0.709. We know the frequency approximates the actual probability, but by how much? More precisely, what are the chances of the actual probability falling within an interval close to 0.709 (such as an interval between 0.7 and 0.71)? To find out, we must do additional sampling.\n","\n","We’ve previously sampled our coin over five iterations of 1,000 coin flips each. The sampling produced some fluctuations in the frequency. Let’s explore these fluctuations by increasing our frequency count from 5 to 500. We can execute this supplementary sampling by running [np.random.binomial(1000, 0.7) for _ in range(500)]."]},{"cell_type":"code","metadata":{"id":"t3h9i5JtDPOU"},"source":["np.random.seed(0)\n","head_count_list = [np.random.binomial(1000, .7) for _ in range(500)]\n","np.random.seed(0)\n","head_count_array = np.random.binomial(1000, 0.7, 500)"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"3ObPE0fRDXmR","executionInfo":{"status":"ok","timestamp":1637255882362,"user_tz":-330,"elapsed":516,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"514705ca-8d9e-44b5-ca5c-7ebab8b8e3e6"},"source":["assert head_count_array.tolist() == head_count_list\n","new_array = np.array(head_count_list)\n","assert np.array_equal(new_array, head_count_array) == True\n","head_count_list[0:10]"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["[697, 690, 700, 707, 702, 699, 723, 670, 702, 713]"]},"metadata":{},"execution_count":60}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"Sx2aWLhNDlU_","executionInfo":{"status":"ok","timestamp":1637255902040,"user_tz":-330,"elapsed":815,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"ffe2396c-f6fa-480e-93c0-716b83f00cc0"},"source":["frequency_array = head_count_array / 1000\n","assert frequency_array.tolist() == [head_count / 1000\n","                                    for head_count in head_count_list]\n","assert frequency_array.tolist() == list(map(lambda x: x / 1000,\n","                                        head_count_list))\n","print(frequency_array[:10])"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["[0.697 0.69  0.7   0.707 0.702 0.699 0.723 0.67  0.702 0.713]\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"iQDS_1m5Dwcl","executionInfo":{"status":"ok","timestamp":1637255943783,"user_tz":-330,"elapsed":448,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"99577713-8695-422c-b6ae-30f27293979a"},"source":["min_freq = frequency_array.min()\n","max_freq = frequency_array.max()\n","print(f\"Minimum frequency observed: {min_freq}\")\n","print(f\"Maximum frequency observed: {max_freq}\")\n","print(f\"Difference across frequency range: {max_freq - min_freq}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Minimum frequency observed: 0.656\n","Maximum frequency observed: 0.733\n","Difference across frequency range: 0.07699999999999996\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"AjMenBbrDwZM","executionInfo":{"status":"ok","timestamp":1637255958396,"user_tz":-330,"elapsed":653,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"3d9d2aef-cb9b-4abc-8a58-a21a549b4450"},"source":["frequency_counts = defaultdict(int)\n","for frequency in frequency_array:\n","    frequency_counts[frequency] += 1\n","\n","frequencies = list(frequency_counts.keys())\n","counts = [frequency_counts[freq] for freq in frequencies]\n","plt.scatter(frequencies, counts)\n","plt.xlabel('Frequency')\n","plt.ylabel('Count')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"ceNQ6nCWDwVc","executionInfo":{"status":"ok","timestamp":1637255977301,"user_tz":-330,"elapsed":568,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"d190c4d7-9b9b-4aae-bcc5-2649fe49ad7b"},"source":["plt.hist(frequency_array, bins='auto', edgecolor='black')\n","plt.xlabel('Binned Frequency')\n","plt.ylabel('Count')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":282},"id":"uWEdsiw7DwRb","executionInfo":{"status":"ok","timestamp":1637255987770,"user_tz":-330,"elapsed":661,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"c18dcf33-452a-438e-aeef-f5d03fddd61a"},"source":["counts, _, _ = plt.hist(frequency_array, bins='auto',\n","                        edgecolor='black')\n","\n","print(f\"Number of Bins: {counts.size}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Number of Bins: 16\n"]},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":282},"id":"-6cdUJOUDwN1","executionInfo":{"status":"ok","timestamp":1637255998591,"user_tz":-330,"elapsed":655,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"f31b4cde-7861-483c-a1db-a1699a76be88"},"source":["counts, bin_edges, _ = plt.hist(frequency_array, bins='auto',\n","                                edgecolor='black')\n","\n","bin_width = bin_edges[1] - bin_edges[0]\n","assert bin_width == (max_freq - min_freq) / counts.size\n","print(f\"Bin width: {bin_width}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Bin width: 0.004812499999999997\n"]},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"XxCuXDxaD-Es","executionInfo":{"status":"ok","timestamp":1637256005290,"user_tz":-330,"elapsed":493,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"3896a6b1-815e-4094-b23b-23423bfe9630"},"source":["def output_bin_coverage(i):\n","    count = int(counts[i])\n","    range_start, range_end = bin_edges[i], bin_edges[i+1]\n","    range_string = f\"{range_start} - {range_end}\"\n","    print((f\"The bin for frequency range {range_string} contains \"\n","           f\"{count} element{'' if count == 1 else 's'}\"))\n","\n","output_bin_coverage(0)\n","output_bin_coverage(5)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["The bin for frequency range 0.656 - 0.6608125 contains 1 element\n","The bin for frequency range 0.6800625 - 0.684875 contains 20 elements\n"]}]},{"cell_type":"code","metadata":{"id":"CHnWMt-mD-Ad"},"source":["assert counts[counts.argmax()] == counts.max()"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"dkPPTJwvD982","executionInfo":{"status":"ok","timestamp":1637256019891,"user_tz":-330,"elapsed":726,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"77b0ce19-1032-4c55-fa9c-513f6e9e8f1d"},"source":["output_bin_coverage(counts.argmax())"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["The bin for frequency range 0.6945 - 0.6993125 contains 72 elements\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":279},"id":"9OVfc3pzD949","executionInfo":{"status":"ok","timestamp":1637256314418,"user_tz":-330,"elapsed":500,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"6d73c151-bdd6-4637-fd58-e506ddcb8be9"},"source":["likelihoods, bin_edges, _ = plt.hist(frequency_array, bins='auto', edgecolor='black', density=True)\n","plt.xlabel('Binned Frequency')\n","plt.ylabel('Relative Likelihood')\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"id":"A-2EK8XYD91D"},"source":["assert likelihoods.sum() * bin_width == 1.0"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"1uhpXZb1FSdp","executionInfo":{"status":"ok","timestamp":1637256346354,"user_tz":-330,"elapsed":478,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"c7568ba0-fa38-44c6-b3b1-f4235929886c"},"source":["index = likelihoods.argmax()\n","area = likelihoods[index] * bin_width\n","range_start, range_end = bin_edges[index], bin_edges[index+1]\n","range_string = f\"{range_start} - {range_end}\"\n","print(f\"Sampled frequency falls within interval {range_string} with probability {area}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Sampled frequency falls within interval 0.6945 - 0.6993125 with probability 0.144\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"pGm_EakkFSaK","executionInfo":{"status":"ok","timestamp":1637256352797,"user_tz":-330,"elapsed":455,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"d29411d7-1322-4059-f803-9c5e68e59edc"},"source":["peak_index = likelihoods.argmax()\n","start_index, end_index = (peak_index - 1, peak_index + 2)\n","area = likelihoods[start_index: end_index + 1].sum() * bin_width\n","range_start, range_end = bin_edges[start_index], bin_edges[end_index]\n","range_string = f\"{range_start} - {range_end}\"\n","print(f\"Sampled frequency falls within interval {range_string} with probability {area}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Sampled frequency falls within interval 0.6896875 - 0.704125 with probability 0.464\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"tCeJHZtrFSWa","executionInfo":{"status":"ok","timestamp":1637256361328,"user_tz":-330,"elapsed":460,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"baa0b010-e18e-46d7-b92c-1dfb5801fa1b"},"source":["def compute_high_confidence_interval(likelihoods, bin_width):\n","    peak_index = likelihoods.argmax()\n","    area = likelihoods[peak_index] * bin_width\n","    start_index, end_index = peak_index, peak_index + 1\n","    while area < 0.95:\n","        if start_index > 0:\n","            start_index -= 1\n","        if end_index < likelihoods.size - 1:\n","            end_index += 1\n","\n","        area = likelihoods[start_index: end_index + 1].sum() * bin_width\n","\n","    range_start, range_end = bin_edges[start_index], bin_edges[end_index]\n","    range_string = f\"{range_start:.6f} - {range_end:.6f}\"\n","    print((f\"The frequency range {range_string} represents a \"\n","           f\"{100 * area:.2f}% confidence interval\"))\n","    return start_index, end_index\n","\n","compute_high_confidence_interval(likelihoods, bin_width)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["The frequency range 0.670438 - 0.723375 represents a 95.40% confidence interval\n"]},{"output_type":"execute_result","data":{"text/plain":["(3, 14)"]},"metadata":{},"execution_count":74}]},{"cell_type":"code","metadata":{"id":"NKIp_O2QFSS4"},"source":["np.random.seed(0)\n","head_count_array = np.random.binomial(1000, 0.7, 100000)\n","frequency_array = head_count_array / 1000\n","assert frequency_array.size == 100000"],"execution_count":null,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":296},"id":"nQZBmuELFSPB","executionInfo":{"status":"ok","timestamp":1637256375035,"user_tz":-330,"elapsed":505,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"cbde15e3-f930-4872-8cd8-2312044ff8bc"},"source":["likelihoods, bin_edges, patches = plt.hist(frequency_array, bins='auto',\n","                                           edgecolor='black', density=True)\n","bin_width = bin_edges[1] - bin_edges[0]\n","start_index, end_index = compute_high_confidence_interval(likelihoods,\n","                                                          bin_width)\n","\n","for i in range(start_index, end_index):\n","     patches[i].set_facecolor('yellow')\n","plt.xlabel('Binned Frequency')\n","plt.ylabel('Relative Likelihood')\n","\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["The frequency range 0.670429 - 0.727857 represents a 95.42% confidence interval\n"]},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":299},"id":"_e1qxp1IFSLB","executionInfo":{"status":"ok","timestamp":1637256382090,"user_tz":-330,"elapsed":535,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"23c46520-e7e1-4ba4-84ac-1d31a9cf2b30"},"source":["np.random.seed(0)\n","head_count_array = np.random.binomial(50000, 0.7, 100000)\n","frequency_array = head_count_array / 50000\n","\n","likelihoods, bin_edges, patches = plt.hist(frequency_array, bins=25,\n","                                           edgecolor='black', density=True)\n","bin_width = bin_edges[1] - bin_edges[0]\n","start_index, end_index = compute_high_confidence_interval(likelihoods,\n","                                                          bin_width)\n","\n","for i in range(start_index, end_index):\n","     patches[i].set_facecolor('yellow')\n","plt.xlabel('Binned Frequency')\n","plt.ylabel('Relative Likelihood')\n","\n","plt.show()"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["The frequency range 0.696229 - 0.704518 represents a 96.22% confidence interval\n"]},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"4sqYAYHZ_fji"},"source":["## Using confidence intervals to analyze a biased deck of cards"]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"JF6Fn9jXFgtD","executionInfo":{"status":"ok","timestamp":1637256402391,"user_tz":-330,"elapsed":569,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"320b3da4-331a-4718-82ce-27639dcda36a"},"source":["np.random.seed(0)\n","\n","likelihoods, bin_edges = np.histogram(frequency_array, bins='auto',\n","                                      density=True)\n","bin_width = bin_edges[1] - bin_edges[0]\n","compute_high_confidence_interval(likelihoods, bin_width)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["The frequency range 0.695769 - 0.703708 represents a 95.06% confidence interval\n"]},{"output_type":"execute_result","data":{"text/plain":["(47, 114)"]},"metadata":{},"execution_count":78}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"dI_U-d_tFyLg","executionInfo":{"status":"ok","timestamp":1637256494089,"user_tz":-330,"elapsed":474,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"e3fb82d3-e5e0-4627-cf46-cdd26b6516b0"},"source":["np.random.seed(0)\n","total_cards = 52\n","red_card_count = np.random.randint(0, total_cards + 1)\n","black_card_count = total_cards - red_card_count\n","assert black_card_count != red_card_count\n","weighted_sample_space = {'red_card': red_card_count,\n","                         'black_card': black_card_count}\n","prob_red = compute_event_probability(lambda x: x == 'red_card',\n","                                     weighted_sample_space)\n","red_card_count"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["44"]},"metadata":{},"execution_count":80}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"7iD17lC0F2zy","executionInfo":{"status":"ok","timestamp":1637256504015,"user_tz":-330,"elapsed":773,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"9a8a48d0-b0d2-4c0c-cfb0-e2957e748341"},"source":["assert prob_red == red_card_count / total_cards\n","np.random.seed(0)\n","color = 'red' if np.random.binomial(1, prob_red) else 'black'\n","print(f\"The first card in the shuffled deck is {color}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["The first card in the shuffled deck is red\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"tL0WT9wXF49d","executionInfo":{"status":"ok","timestamp":1637256524337,"user_tz":-330,"elapsed":529,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"e9ad394d-8ccf-40ec-c921-2191273dd2a8"},"source":["np.random.seed(0)\n","red_count = np.random.binomial(10, prob_red)\n","print(f\"In {red_count} of out 10 shuffles, a red card came up first.\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["In 8 of out 10 shuffles, a red card came up first.\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"FtshU09NFqQ8","executionInfo":{"status":"ok","timestamp":1637256532725,"user_tz":-330,"elapsed":517,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"b76fa15d-878d-408c-cdb8-07ecb502060d"},"source":["np.random.seed(0)\n","red_card_count_array = np.random.binomial(50000, prob_red, 100000)\n","frequency_array = red_card_count_array / 50000\n","\n","likelihoods, bin_edges = np.histogram(frequency_array, bins='auto',\n","                                      density=True)\n","bin_width = bin_edges[1] - bin_edges[0]\n","start_index, end_index = compute_high_confidence_interval(likelihoods,\n","                                                          bin_width)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["The frequency range 0.842865 - 0.849139 represents a 95.16% confidence interval\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"uvFl_pT0FsIO","executionInfo":{"status":"ok","timestamp":1637256552899,"user_tz":-330,"elapsed":519,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"f74a816d-9442-46d9-91f9-94c5f596ab81"},"source":["range_start = round(0.842771 * total_cards)\n","range_end = round(0.849139 * total_cards)\n","print(f\"The number of red cards in the deck is between {range_start} and {range_end}\")\n","\n","if red_card_count == 44:\n","    print('We are correct! There are 44 red cards in the deck')\n","else:\n","    print('Oops! Our sampling estimation was wrong.')"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["The number of red cards in the deck is between 44 and 44\n","We are correct! There are 44 red cards in the deck\n"]}]},{"cell_type":"markdown","metadata":{"id":"uWjbBQNxCKs-"},"source":["## Using permutations to shuffle cards"]},{"cell_type":"markdown","metadata":{"id":"EBJBkEL2GMjc"},"source":["Card shuffling requires us to randomly reorder the elements of a card deck. That random reordering can be carried out using the np.random.shuffle method. The function takes as input an ordered array or list and shuffles its elements in place. The following code randomly shuffles a deck of cards containing two red cards (represented by 1s) and two black cards (represented by 0s)."]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"xOH0zVyYGM0a","executionInfo":{"status":"ok","timestamp":1637256591877,"user_tz":-330,"elapsed":489,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"8298c5d6-d1ef-4ad3-9e03-8dd7a2eaa4ee"},"source":["np.random.seed(0)\n","card_deck = [1, 1, 0, 0]\n","np.random.shuffle(card_deck)\n","print(card_deck)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["[0, 0, 1, 1]\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"ctflfV-6GPTX","executionInfo":{"status":"ok","timestamp":1637256598220,"user_tz":-330,"elapsed":695,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"2bb0a8a5-0229-4667-9bbd-2e0082b330b4"},"source":["np.random.seed(0)\n","unshuffled_deck = [1, 1, 0, 0]\n","shuffled_deck = np.random.permutation(unshuffled_deck)\n","assert unshuffled_deck == [1, 1, 0, 0]\n","print(shuffled_deck)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["[0 0 1 1]\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"kIJGyKeoGQwh","executionInfo":{"status":"ok","timestamp":1637256603896,"user_tz":-330,"elapsed":489,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"e0247d11-0a07-4d4e-99fb-95c308562b26"},"source":["import itertools\n","for permutation in list(itertools.permutations(unshuffled_deck))[:3]:\n","    print(permutation)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["(1, 1, 0, 0)\n","(1, 1, 0, 0)\n","(1, 0, 1, 0)\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"6aXZ8U2DGSO-","executionInfo":{"status":"ok","timestamp":1637256609297,"user_tz":-330,"elapsed":670,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"2b9ff053-9bad-4814-a0cf-7078185119ec"},"source":["for permutation in list(itertools.permutations([0, 1, 2, 3]))[:3]:\n","    print(permutation)"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["(0, 1, 2, 3)\n","(0, 1, 3, 2)\n","(0, 2, 1, 3)\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"96wGVBLNGTeC","executionInfo":{"status":"ok","timestamp":1637256614953,"user_tz":-330,"elapsed":555,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"74cb1964-9717-4710-8e38-57579f49f40a"},"source":["weighted_sample_space = defaultdict(int)\n","for permutation in itertools.permutations(unshuffled_deck):\n","    weighted_sample_space[permutation] += 1\n","\n","for permutation, count in weighted_sample_space.items():\n","    print(f\"Permutation {permutation} occurs {count} times\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Permutation (1, 1, 0, 0) occurs 4 times\n","Permutation (1, 0, 1, 0) occurs 4 times\n","Permutation (1, 0, 0, 1) occurs 4 times\n","Permutation (0, 1, 1, 0) occurs 4 times\n","Permutation (0, 1, 0, 1) occurs 4 times\n","Permutation (0, 0, 1, 1) occurs 4 times\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"O2ZejIlpGU1Q","executionInfo":{"status":"ok","timestamp":1637256675090,"user_tz":-330,"elapsed":444,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"2ec8222d-1b69-498c-c758-324ed17db6bc"},"source":["sample_space = set(itertools.permutations(unshuffled_deck))\n","event_condition = lambda x: list(x) == unshuffled_deck\n","prob = compute_event_probability(event_condition, sample_space)\n","assert prob == 1 / len(sample_space)\n","print(f\"Probability that a shuffle does not alter the deck is {prob}\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Probability that a shuffle does not alter the deck is 0.16666666666666666\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"T0HsSwfQGjpN","executionInfo":{"status":"ok","timestamp":1637256678760,"user_tz":-330,"elapsed":893,"user":{"displayName":"Sparsh Agarwal","photoUrl":"https://lh3.googleusercontent.com/a/default-user=s64","userId":"13037694610922482904"}},"outputId":"85fe2db8-df50-477a-b44c-7d2be619b7a0"},"source":["red_cards = 5 * [1]\n","black_cards = 5 * [0]\n","unshuffled_deck = red_cards + black_cards\n","sample_space = set(itertools.permutations(unshuffled_deck))\n","print(f\"Sample space for a 10-card deck contains {len(sample_space)} elements\")"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["Sample space for a 10-card deck contains 252 elements\n"]}]},{"cell_type":"markdown","metadata":{"id":"JPh4pgW6GkSd"},"source":["**END**"]}]}