Python Puzzles
Imagine a bag that contains a single ball, which has an equal probability of being either black or white. Now, add a white ball to this bag. At this point, the bag holds two balls: one white and another that could be either white or black, each with an equal chance of 50%. If you randomly draw one ball from the bag, what would be the likelihood that the remaining ball inside the bag is white, given that you’ve drawn a white ball?
Don’t overcomplicate this conundrum; the probability that the remaining ball in the bag is white will be 50%.
Here is the Python code to run a simulation.
import random
# number of simulations
num_simulations = 1000000
# counter for the number of times the remaining ball is white given that a white ball was drawn
count_white_remain = 0
for _ in range(num_simulations):
# initial bag has a white ball and a ball that is equally likely to be black or white
bag = ['white', random.choice(['white', 'black'])]
# draw a ball
drawn_ball = random.choice(bag)
# if the drawn ball is white, remove it and check the color of the remaining ball
if drawn_ball == 'white':
bag.remove(drawn_ball)
if bag[0] == 'white':
count_white_remain += 1
# probability that the ball left in the bag is white given that a white ball was drawn
prob_white_remain = count_white_remain / num_simulations
print('Probability that the remaining ball is white given that a white ball was drawn:', prob_white_remain)