2017 AMC 10A Problem 18

Amelia has a coin that lands heads with probability \tfrac{1}{3}, and Blaine has a coin that lands on heads with probability \tfrac{2}{5}. Amelia and Blaine alternately toss their coins until someone gets a head; the first one to get a head wins. All coin tosses are independent. Amelia goes first. The probability that Amelia wins is \tfrac{p}{q}, where p and q are relatively prime positive integers. What is q-p?

\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.