FERMAT 2015 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?

Answer Choices
A. \frac{21}{32}
B. \frac58
C. \frac37
D. \frac{11}{16}
E. \frac{9}{16}