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Omni-MATH / Alice draws three cards from a standard 52-card deck with replacement. Ace…

Problem

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problem

Alice draws three cards from a standard 52-card deck with replacement. Ace through 10 are worth 1 to 10 points respectively, and the face cards King, Queen, and Jack are each worth 10 points. The probability that the sum of the point values of the cards drawn is a multiple of 10 can be written as mn\frac{m}{n}, where m,nm, n are positive integers and gcd(m,n)=1\operatorname{gcd}(m, n)=1. Find 100m+n100 m+n.
Plain-text mathematical notation (without MathML)
Alice draws three cards from a standard 52-card deck with replacement. Ace through 10 are worth 1 to 10 points respectively, and the face cards King, Queen, and Jack are each worth 10 points. The probability that the sum of the point values of the cards drawn is a multiple of 10 can be written as (m)/(n), where m,n are positive integers and gcd(m,n)=1. Find 100m+n.
Original LaTeX notation
Alice draws three cards from a standard 52-card deck with replacement. Ace through 10 are worth 1 to 10 points respectively, and the face cards King, Queen, and Jack are each worth 10 points. The probability that the sum of the point values of the cards drawn is a multiple of 10 can be written as $\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n)=1$. Find $100 m+n$.

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Source and history

task_id
b762eae9-eea4-5c82-b453-4356140b6b37
task_key
test--b762eae9-eea4-5c82-b453-4356140b6b37
task_revision_id
1
config / split
/ test

Official source

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