# Difference between revisions of "2019 AIME II Problems/Problem 2"

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

## Revision as of 14:52, 22 March 2019

Lily pads lie in a row on a pond. A frog makes a sequence of jumps starting on pad . From any pad the frog jumps to either pad or pad chosen randomly with probability and independently of other jumps. The probability that the frog visits pad is , where and are relatively prime positive integers. Find .