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Omni-MATH / Carina is in a tournament in which no game can end in a tie. She continues to…

Problem

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problem

Carina is in a tournament in which no game can end in a tie. She continues to play games until she loses 2 games, at which point she is eliminated and plays no more games. The probability of Carina winning the first game is rac12 rac{1}{2}. After she wins a game, the probability of Carina winning the next game is rac34 rac{3}{4}. After she loses a game, the probability of Carina winning the next game is rac13 rac{1}{3}. What is the probability that Carina wins 3 games before being eliminated from the tournament?
Plain-text mathematical notation (without MathML)
Carina is in a tournament in which no game can end in a tie. She continues to play games until she loses 2 games, at which point she is eliminated and plays no more games. The probability of Carina winning the first game is rac12. After she wins a game, the probability of Carina winning the next game is rac34. After she loses a game, the probability of Carina winning the next game is rac13. What is the probability that Carina wins 3 games before being eliminated from the tournament?
Original LaTeX notation
Carina is in a tournament in which no game can end in a tie. She continues to play games until she loses 2 games, at which point she is eliminated and plays no more games. The probability of Carina winning the first game is $rac{1}{2}$. After she wins a game, the probability of Carina winning the next game is $rac{3}{4}$. After she loses a game, the probability of Carina winning the next game is $rac{1}{3}$. What is the probability that Carina wins 3 games before being eliminated from the tournament?

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Source and history

task_id
d63a2e0e-6292-5c2f-a6bd-cce385b9995b
task_key
test--d63a2e0e-6292-5c2f-a6bd-cce385b9995b
task_revision_id
1
config / split
/ test

Official source

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