2019 AIME II Problems/Problem 2

Revision as of 14:52, 22 March 2019 by Thothdragonfly2 (talk | contribs)

Lily pads $1,2,3,\ldots$ lie in a row on a pond. A frog makes a sequence of jumps starting on pad $1$. From any pad $k$ the frog jumps to either pad $k+1$ or pad $k+2$ chosen randomly with probability $\tfrac12$ and independently of other jumps. The probability that the frog visits pad $7$ is $\tfrac pq$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.

Invalid username
Login to AoPS