Problem:
Tom, Dick, and Harry are playing a game. Starting at the same time, each of them flips a fair coin repeatedly until he gets his first head, at which point he stops. What is the probability that all three flip their coins the same number of times?
Answer Choices:
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Solution:
The probability that a flipper obtains his first head on the flip is , because the sequence of outcomes must be exactly TT ...TH, with Ts. Therefore the probability that all of them obtain their first heads on the flip is . The probability that all three flip their coins the same number of times is computed by summing an infinite geometric series:
The problems on this page are the property of the MAA's American Mathematics Competitions