There are two urns: Urn 1 contains two red balls and one black ball, and Urn 2 has 101 red balls and 100 black balls. Two balls can be taken from one of the urns at random. The task is to correctly identify the urn from which the balls have been collected. After the first draw, you can decide whether to replace the ball. What will be your strategy?
If the first ball is red, the remaining balls in Urn 1 are one red and one black, and in Urn 2, 100 red and 100 black. That means the probability of drawing any colour is equal (0.5) from each urn. As this can’t help deciding the correct urn, return the red ball and pull the second ball.
If the first ball is black, the remaining balls in Urn 1 are two reds and zero black, and in Urn 2 are 101 red and 99 black. In such a case, do not replace the ball, as the probabilities of red and black are different in each urn, which helps identify the urn better.
