**Python Puzzles**

You have two dice; one is fair and the other unfair. The unfair dice rolls a 6 50% of the time.

What is the probability of choosing the unfair dice if you randomly choose a dice and roll a 6?

You can use Bayes theorem to provide a mathematical proof.

- The probability of the dice being unfair is 75%.
- The probability of the dice being fair is 25%.

import random # initialize variables to count the number of times each dice is selected unfair_dice = 0 fair_dice = 0 # initialize an empty list to hold the results list = [] # simulate 10,000 rolls of a dice for _ in range(10_000): # randomly choose a dice, either 1 or 2 dice = random.randrange(1,3); # dice 1 is unfair if dice == 1: # Probability of rolling a 6 is 50% diceroll = random.randrange(5,7) if diceroll == 6: list.append(dice) # dice 2 is fair if dice == 2: diceroll = random.randrange(1,7) if diceroll == 6: list.append(dice) # determine the proportion of rolls for each dice for x in list: if x == 1: unfair_dice = unfair_dice + 1 else: fair_dice = fair_dice + 1 # print the probabilities of each dice being selected print('The probability of the dice being fair is ' + '{0:.1%}'.format(fair_dice/len(list))) print('The probability of the dice being unfair is ' + '{0:.1%}'.format(unfair_dice/len(list)))