Question

A paper bag contains a mixture of three types of treats: 12 granola bars, 10 fruit bars, and 8 cheese strips. Suppose that you play a game in which a treat is randomly taken from the bag and replaced, and then a second treat is drawn from the bag. You are allowed to keep the second treat only if it was the same type as the treat that was drawn the first time. Determine the probability that you will be able to keep a fruit bar. Use set notation in your solution.

Answer 1

success if you draw 2 granolas or 2 fruits or 2 cheese

prob(success) = (12/30)(12/30) + (10/30)(10/30) + (8/30)(8/30
= 4/25 + 1/9 + 16/225
= 77/225