benchmarks.wiki / Public workspace
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Omni-MATH / Diana is playing a card game against a computer. She starts with a deck…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
problem
Diana is playing a card game against a computer. She starts with a deck consisting of a single card labeled 0.9. Each turn, Diana draws a random card from her deck, while the computer generates a card with a random real number drawn uniformly from the interval . If the number on Diana's card is larger, she keeps her current card and also adds the computer's card to her deck. Otherwise, the computer takes Diana's card. After turns, Diana's deck is empty. Compute the expected value of .
Plain-text mathematical notation (without MathML)
Diana is playing a card game against a computer. She starts with a deck consisting of a single card labeled 0.9. Each turn, Diana draws a random card from her deck, while the computer generates a card with a random real number drawn uniformly from the interval [0,1]. If the number on Diana's card is larger, she keeps her current card and also adds the computer's card to her deck. Otherwise, the computer takes Diana's card. After k turns, Diana's deck is empty. Compute the expected value of k.
Original LaTeX notation
Diana is playing a card game against a computer. She starts with a deck consisting of a single card labeled 0.9. Each turn, Diana draws a random card from her deck, while the computer generates a card with a random real number drawn uniformly from the interval $[0,1]$. If the number on Diana's card is larger, she keeps her current card and also adds the computer's card to her deck. Otherwise, the computer takes Diana's card. After $k$ turns, Diana's deck is empty. Compute the expected value of $k$.
Discussion
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Source and history
- task_id
e2ed80d6-75e9-5f59-900c-8aef5f6dd93b- task_key
test--e2ed80d6-75e9-5f59-900c-8aef5f6dd93b- task_revision_id
- 1
- config / split
- / test
initial import