Question

Given 3 urns, one contains 2 black balls, the second contains 2 white balls, and the third contains 1 ball of each color. An
urn is chosen at random and a ball is drawn from it -- the ball is white. What is the probability that the other ball in that urn is also white?

Answer 1

Let the urn has 2 black balls, urn has white balls and urn has one white and 1 black ball.

Define the events.

Then,

Using total probability theorem,

When other ball in that urn is also white is the urn was chosen.

The required conditional probability is