"""
problem1.py
====

Author:  


Module 3 (https://cs.nyu.edu/elearning/CSCI_UA_0002/module03.php) contained some 
discussion about generating random numbers.

Read and understand the code of a program. The program uses random numbers to 
simulate rolling of a six-sided die and then prints the report and shows a plot of
the probability distribution function. 

Answer the questions below the program and change the code according to instructions
in the last question. 


    
"""
import matplotlib.pyplot as plt
import random

num_of_repeats = int(input("How many times should I roll the die? \n"))
num_of_sides  = 6 

print("Rolling", num_of_repeats, "times.")

# list all possible outcomes 
outcomes = [1,2,3,4,5,6]
# initialize counts to zero 
counts = [0]*num_of_sides

# simulate rolling the die 
for i in range(num_of_repeats) :
    # roll the virtual die
    die = random.randint(1,num_of_sides) 
    # increment appropriate count
    counts[die-1] += 1 


# print the report 
for i in range(num_of_sides) :
    #calculate fraction of rolls for each value 
    counts[i] = counts[i]/num_of_repeats
    #print the results 
    print(i+1, " was rolled ", counts[i], " many times (", 
            counts[i]*100, "% of times)", sep = "")
 


plt.plot(outcomes, counts)
axes = plt.gca()
axes.set_ylim([0,1]) 
plt.show()
       
'''
How many times does the program have to roll a die to get almost the 
same number of rolls of each value (the percent should be the same, except for the
fraction part)? 

ANSWER:
    
    

    
In the plot generated by the above program, what happens to the shape
of the graph as the number of rolls increases? (run the program several times with
different number of rolls and watch what happens to the line) 

ANSWER:             

    
If we could plot the true probability distribution for this experiment, what do you
think the shape of the plot would be? 

ANSWER: 
    
                    
                

What do you need to change in the above program so that it simulates
rolling of a 5-sided die? (Show the modified lines as part of your answer.)

ANSWER: 
    
    
    
    
What do you need to change in the above program so that it does not simulate a fair die, 
but instead the values of 1, 2 and 3 are twice as likely as the values of 4, 5, and 6?
Make the changes in the program and submit a mofied version. 
The output of your mofied program should be similar to:
-----    
How many times should I roll the die? 
1000000
Rolling 1000000 times.
1 was rolled .222099 many times (22.209899999999998% of times)
2 was rolled .221374 many times (22.1374% of times)
3 was rolled .222807 many times (22.2807% of times)
4 was rolled .111084 many times (11.1084% of times)
5 was rolled .111599 many times (11.1599% of times)
6 was rolled .111037 many times (11.1037% of times)
-----



'''