2022 SSMO Accuracy Round Problems/Problem 6

Problem

Consider an unfair $6$ -sided die labeled from $1$ to $6$ , such that the probability of rolling a number $m$ is directly proportional to $7-m$ . However, if we roll any number $n$ , then the probability of rolling a number less than $n$ becomes $0$ , and the probability of rolling any number $m$ from $n$ to $6$ inclusive remains directly proportional to $7-m$ . The expected number of rolls until a $6$ is rolled can be expressed as $\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

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2022 SSMO Accuracy Round Problems/Problem 6

Problem

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