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MATH / When rolling a certain unfair six-sided die with faces numbered 1, 2, 3, 4, 5,…

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problem

When rolling a certain unfair six-sided die with faces numbered 1, 2, 3, 4, 5, and 6, the probability of obtaining face FF is greater than 1/61/6, the probability of obtaining the face opposite face FF is less than 1/61/6, the probability of obtaining each of the other faces is 1/61/6, and the sum of the numbers on each pair of opposite faces is 7. When two such dice are rolled, the probability of obtaining a sum of 7 is 47288 \frac{47}{288} . Given that the probability of obtaining face FF is m/nm/n, where mm and nn are relatively prime positive integers, find m+nm+n.
Plain-text mathematical notation (without MathML)
When rolling a certain unfair six-sided die with faces numbered 1, 2, 3, 4, 5, and 6, the probability of obtaining face F is greater than 1/6, the probability of obtaining the face opposite face F is less than 1/6, the probability of obtaining each of the other faces is 1/6, and the sum of the numbers on each pair of opposite faces is 7. When two such dice are rolled, the probability of obtaining a sum of 7 is (47)/(288). Given that the probability of obtaining face F is m/n, where m and n are relatively prime positive integers, find m+n.
Original LaTeX notation
When rolling a certain unfair six-sided die with faces numbered 1, 2, 3, 4, 5, and 6, the probability of obtaining face $F$ is greater than $1/6$, the probability of obtaining the face opposite face $F$ is less than $1/6$, the probability of obtaining each of the other faces is $1/6$, and the sum of the numbers on each pair of opposite faces is 7. When two such dice are rolled, the probability of obtaining a sum of 7 is $ \frac{47}{288} $. Given that the probability of obtaining face $F$ is $m/n$, where $m$ and $n$ are relatively prime positive integers, find $m+n$.

level

Level 5

type

Counting & Probability

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Source and history

task_id
5caff8d8-8a03-5348-85bd-b1612ec9bb4c
task_key
counting~5fand~5fprobability--test--5caff8d8-8a03-5348-85bd-b1612ec9bb4c
task_revision_id
1
config / split
counting_and_probability / test

Official source

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