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AIME 2024 / AIME 2024 train 5c12cbcd-9796-5706-aa4d-66b05e046e23

Problem

Answer published by the source. Consult the official source to check your work against its answer.

Problem

Jen enters a lottery by picking

4

distinct numbers from

S=\{1,2,3,\cdots,9,10\}.

4

numbers are randomly chosen from

S.

She wins a prize if at least two of her numbers were

2

of the randomly chosen numbers, and wins the grand prize if all four of her numbers were the randomly chosen numbers. The probability of her winning the grand prize given that she won a prize is

\tfrac{m}{n}

where

m

and

n

are relatively prime positive integers. Find

m+n

Plain-text mathematical notation (without MathML)

Jen enters a lottery by picking 4 distinct numbers from S={1,2,3,⋯,9,10}. 4 numbers are randomly chosen from S. She wins a prize if at least two of her numbers were 2 of the randomly chosen numbers, and wins the grand prize if all four of her numbers were the randomly chosen numbers. The probability of her winning the grand prize given that she won a prize is (m)/(n) where m and n are relatively prime positive integers. Find m+n.

Original LaTeX notation

Jen enters a lottery by picking $4$ distinct numbers from $S=\{1,2,3,\cdots,9,10\}.$ $4$ numbers are randomly chosen from $S.$ She wins a prize if at least two of her numbers were $2$ of the randomly chosen numbers, and wins the grand prize if all four of her numbers were the randomly chosen numbers. The probability of her winning the grand prize given that she won a prize is $\tfrac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

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Source and history

task_id: 5c12cbcd-9796-5706-aa4d-66b05e046e23
task_key: default--train--5c12cbcd-9796-5706-aa4d-66b05e046e23
task_revision_id: 2
config / split: default / train

Official source

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