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2019 AIME II Problems/Problem 2

Revision as of 16:56, 22 March 2019 by Brendanb4321 (talk | contribs)

Problem

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 $p+q$.

Solution

See Also

2019 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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