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Omni-MATH / A standard n-sided die has n sides labeled 1 to n. Luis, Luke, and Sean play a game in which they roll a fair standard 4-sided die, a fair standard 6-sided die, and a fair standard…

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problem

A standard nn-sided die has nn sides labeled 1 to nn. Luis, Luke, and Sean play a game in which they roll a fair standard 4-sided die, a fair standard 6-sided die, and a fair standard 8-sided die, respectively. They lose the game if Luis's roll is less than Luke's roll, and Luke's roll is less than Sean's roll. Compute the probability that they lose the game.
Plain-text mathematical notation (without MathML)
A standard n-sided die has n sides labeled 1 to n. Luis, Luke, and Sean play a game in which they roll a fair standard 4-sided die, a fair standard 6-sided die, and a fair standard 8-sided die, respectively. They lose the game if Luis's roll is less than Luke's roll, and Luke's roll is less than Sean's roll. Compute the probability that they lose the game.
Original LaTeX notation
A standard $n$-sided die has $n$ sides labeled 1 to $n$. Luis, Luke, and Sean play a game in which they roll a fair standard 4-sided die, a fair standard 6-sided die, and a fair standard 8-sided die, respectively. They lose the game if Luis's roll is less than Luke's roll, and Luke's roll is less than Sean's roll. Compute the probability that they lose the game.

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Source and history

task_id
debcb5d3-6fcd-590b-9b34-72b07ae41e7d
task_key
test--debcb5d3-6fcd-590b-9b34-72b07ae41e7d
task_revision_id
1
config / split
/ test

Official source

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