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Omni-MATH / Crisp All, a basketball player, is dropping dimes and nickels on a number line.…

Problem

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problem

Crisp All, a basketball player, is dropping dimes and nickels on a number line. Crisp drops a dime on every positive multiple of 10 , and a nickel on every multiple of 5 that is not a multiple of 10. Crisp then starts at 0 . Every second, he has a 23\frac{2}{3} chance of jumping from his current location xx to x+3x+3, and a 13\frac{1}{3} chance of jumping from his current location xx to x+7x+7. When Crisp jumps on either a dime or a nickel, he stops jumping. What is the probability that Crisp stops on a dime?
Plain-text mathematical notation (without MathML)
Crisp All, a basketball player, is dropping dimes and nickels on a number line. Crisp drops a dime on every positive multiple of 10 , and a nickel on every multiple of 5 that is not a multiple of 10. Crisp then starts at 0 . Every second, he has a (2)/(3) chance of jumping from his current location x to x+3, and a (1)/(3) chance of jumping from his current location x to x+7. When Crisp jumps on either a dime or a nickel, he stops jumping. What is the probability that Crisp stops on a dime?
Original LaTeX notation
Crisp All, a basketball player, is dropping dimes and nickels on a number line. Crisp drops a dime on every positive multiple of 10 , and a nickel on every multiple of 5 that is not a multiple of 10. Crisp then starts at 0 . Every second, he has a $\frac{2}{3}$ chance of jumping from his current location $x$ to $x+3$, and a $\frac{1}{3}$ chance of jumping from his current location $x$ to $x+7$. When Crisp jumps on either a dime or a nickel, he stops jumping. What is the probability that Crisp stops on a dime?

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Source and history

task_id
5e49d444-ba3f-5d1d-97fa-912682ed8bdd
task_key
test--5e49d444-ba3f-5d1d-97fa-912682ed8bdd
task_revision_id
1
config / split
/ test

Official source

initial import