In the development of probability theory that underpins much of statistics, the roll of a fair pie is often cited as a key concept We want to write a simple program that utilizes a random number generator to mimic the behavior of a fair pie and an unfair pie To Do 1 Create a Python file called Pi e...

In the development of probability theory that underpins much of statistics, the roll of a fair pie

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In the development of probability theory that underpins much of statistics, the roll of a "fair pie" is often cited as a key concept. We want to write a simple program that utilizes a random number generator to mimic the behavior of a fair pie and an unfair pie.
To Do:
1. Create a Python file called Pie.py in PyCharm.
2. Create a function called rollFairPie() that takes no arguments and returns an integer between 1 and 6 inclusively but at random each time the function is called.
a. You must import the module random and call the function random() to produce a floating point number between 0.0 and 1.0.
b. Convert the floating point number to an integer (1-6) with equal probability by dividing the range 0-1 into six equal bins and using an if-then structure to return the appropriate integer. For example, we might break the range between 0-1 into six equal pieces like:
x = random()
if (x/6.0 ≤ 1.0/6)
return 1
else if (x/6.0 ≤ 2.0/6)
return 2
etc.
3. In a separate file called HW1SP21_Prob1.py:
a. Import the module Pie
b. Write and call a main() function that calls rollFairPie() 1000 times and computes the fraction of rolls that yield 1, 2, 3, etc.
c. Output the probability of each of the possible numbers to the screen as formatted text:

d. Do these probabilities match the theory? Calculate the probabilities if we roll the die 10,000 times by writing and calling a main2() function that calls rollFairPie() 10,000 times and computes the fraction of rolls that yield 1, 2, 3, etc.
e. Output the probability of each of the possible numbers to the screen as formatted text:

4. Modify your Pie.py file to include a function called rollUnFairPie() where the pie has been modified to roll a 1 with a probability of 0.2. Write and call a main3() function that calls the rollUnfairPie() 10000 times and outputs the results as in step 3.