Question

Elizabeth brought a box of donuts to share. There are​ two-dozen (24) donuts in the​ box, all identical in​ size, shape, and color.  Five are​ jelly-filled, 5 are​ lemon-filled, and 14 are​ custard-filled. You randomly select one​ donut, eat​ it, and select another donut. Find the probability of selecting two jelly ​-filled donuts in a row.

Answer 1

This is a probability problem with two dependent events and conditional probability. Note that after the first donut is chosen, it is not replaced into the data set, so only 23 donuts remain. If we set A=selection of a lemon-filled, and B=selection of a custard-filled, then P(A and B) = P(A)*P(B|A), where P(B|A) means the probability of B happening given that A has already occurred.P(A) = 8/24 = 1/3 = 0.333333P(B|A) = 12/23 = 0.521739P(A and B) = 1/3(12/23) = 12/69 = 0.1739130435 or 17.4%

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