MathDB
Debra's Coin

Source: 2019 AMC 10 B #21

February 14, 2019
2019 AMCAMCAMC 102019 AMC 10Bprobability

Problem Statement

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?
<spanclass=latexbold>(A)</span>136<spanclass=latexbold>(B)</span>124<spanclass=latexbold>(C)</span>118<spanclass=latexbold>(D)</span>112<spanclass=latexbold>(E)</span>16<span class='latex-bold'>(A) </span> \frac{1}{36} \qquad <span class='latex-bold'>(B) </span> \frac{1}{24} \qquad <span class='latex-bold'>(C) </span> \frac{1}{18} \qquad <span class='latex-bold'>(D) </span> \frac{1}{12} \qquad <span class='latex-bold'>(E) </span> \frac{1}{6}