2015 Fermat Problem 21

Amina and Bert alternate turns tossing a fair coin. Amina goes first and each player takes three turns. The first player to toss a tail wins. If neither Amina nor Bert tosses a tail, then neither wins. What is the probability that Amina wins?

\textbf{(A)}\ \frac{21}{32}\quad \textbf{(B)}\ \frac{5}{8}\quad \textbf{(C)}\ \frac{3}{7}\quad \textbf{(D)}\ \frac{11}{16}\quad \textbf{(E)}\ \frac{9}{16}

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Full credit to this problem is given to the CEMC, you may view all Fermat contests here.