Problem:
Debra flips a fair coin repeatedly, keeping track of how many heads and how many tails she has seen in total, until she gets either two heads in a row or two tails in a row, at which point she stops flipping. What is the probability that she gets two heads in a row but she sees a second tail before she sees a second head?
Answer Choices:
A.
B.
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D.
E.
Solution:
With probability , either or will occur after a finite number of flips. The desired event will occur if and only if the sequence of flips is THTHH or or or ... The probabilities of these outcomes are , a geometric sequence with common ratio . The requested probability is the sum of these probabilities,
The problems on this page are the property of the MAA's American Mathematics Competitions