Puzzle of the day

Question:

You have two identical boxes, each containing two balls. One box contains two black balls, and the other box contains one black ball and one white ball. You pick a box at random and pick a ball at random. The ball is black. What is the probability that the other ball in the same box is also black?

Answer:

2/3

Explanation:

Since the picked ball is black, there are two possibilities: 1. The box picked was the one with two black balls, and the probability of this is 1/2. In this case, the other ball is also black. 2. The box picked was the one with one black and one white ball, and the probability of this is also 1/2. However, in this case, the other ball is white.

Therefore, the probability that the other ball is black is 1/2 (from possibility 1) divided by the probability of choosing the correct box (1/2), which equals 1/2 or 2/3.