2006 AMC 10B Problem 17
Problem 17 of 25IntermediateCounting & Probability
Bob and Alice each have a bag that contains one ball of each of the colors blue, green, orange, red, and violet. Alice randomly selects one ball from her bag and puts it into Bob’s bag. Bob then randomly selects one ball from his bag and puts it into Alice’s bag. What is the probability that after this process the contents of the two bags are the same?
Answer choices
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Solution
Alice moves one ball to Bob, so Bob’s bag holds balls with exactly one color appearing twice.
The two bags end up identical exactly when Bob returns one of that duplicated pair. Two of the six balls qualify, so the probability is
Thus, the correct answer is D.