{"status": "success", "data": {"description_md": "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 and independently with probability $\\tfrac12$. The probability that the frog visits pad $7$ is $\\tfrac pq$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

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 and independently with probability \\tfrac12. The probability that the frog visits pad 7 is \\tfrac pq, where p and q are relatively prime positive integers. Find p+q.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2019 AIME II Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/19_aime_II_p03", "prev": "/problem/19_aime_II_p01"}}