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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_5 / Janet rolls a standard 6-sided die 4 times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal 3? The final…

Problem

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problem

Janet rolls a standard

6

-sided die

4

times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal

3

? The final answer can be written in the form

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. What is

m+n

Plain-text mathematical notation (without MathML)

Janet rolls a standard 6-sided die 4 times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal 3? The final answer can be written in the form (m)/(n), where m and n are relatively prime positive integers. What is m+n?

Original LaTeX notation

Janet rolls a standard $6$-sided die $4$ times and keeps a running total of the numbers she rolls. What is the probability that at some point, her running total will equal $3$? The final answer can be written in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_5
task_id: 9670bafe-5c31-53d6-835d-0cbc8a590680
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f5
task_revision_id: 2
config / split: default / train

Official source

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