A chess set has 16 white pieces and 16 black pieces.Suppose that you are blindly removing chess pieces from a bag.What is the probability that the first two pieces you remove will both be black or both be white?

Question

Quizplus · Accepted Answer

There are a total of 32 pieces in the bag, so the probability of selecting a black piece on the first pick is 16/32 = 1/2. If a black piece is selected on the first pick, there are 31 pieces left in the bag, including 15 black pieces and 16 white pieces. So the probability of selecting another black piece on the second pick is 15/31. Similarly, if a white piece is selected on the first pick, there are still 31 pieces left in the bag, including 16 black pieces and 15 white pieces. So the probability of selecting another white piece on the second pick is 15/31. Therefore, the probability of selecting two black pieces or two white pieces is (1/2)(15/31) + (1/2)(15/31) = 15/31.

A Chess Set Has 16 White Pieces and 16 Black