Thread: 50 black and 50 white ball probability problem

Problem Statement:

There are two empty urns in a room. You have 50 white balls and 50 black balls. After you place the balls in the urns, a random ball will be picked from a random urn. Distribute the balls (all of them) into the urns to maximize the chance of picking a white ball.

Solution:

Place one white in one urn, and all the others in the other urn. This gives a 74/99 probability of picking white.

explanation:

probability of picking white ball from which only one white ball is there = 1
probability of picking white ball from which 49 white and 50 black ball is there = 49/99

probability of picking white ball = (1 + 49/99)/2