57 lines
1.6 KiB
Markdown
57 lines
1.6 KiB
Markdown
---
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id: 5900f5221000cf542c510033
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title: 'Problem 436: Unfair wager'
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challengeType: 5
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forumTopicId: 302107
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dashedName: problem-436-unfair-wager
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---
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# --description--
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Julie proposes the following wager to her sister Louise.
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She suggests they play a game of chance to determine who will wash the dishes.
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For this game, they shall use a generator of independent random numbers uniformly distributed between 0 and 1.
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The game starts with $S = 0$.
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The first player, Louise, adds to $S$ different random numbers from the generator until $S > 1$ and records her last random number '$x$'.
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The second player, Julie, continues adding to $S$ different random numbers from the generator until $S > 2$ and records her last random number '$y$'.
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The player with the highest number wins and the loser washes the dishes, i.e. if $y > x$ the second player wins.
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For example, if the first player draws 0.62 and 0.44, the first player turn ends since $0.62 + 0.44 > 1$ and $x = 0.44$. If the second players draws 0.1, 0.27 and 0.91, the second player turn ends since $0.62 + 0.44 + 0.1 + 0.27 + 0.91 > 2$ and $y = 0.91$. Since $y > x$, the second player wins.
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Louise thinks about it for a second, and objects: "That's not fair".
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What is the probability that the second player wins? Give your answer rounded to 10 places behind the decimal point in the form 0.abcdefghij
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# --hints--
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`unfairWager()` should return `0.5276662759`.
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```js
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assert.strictEqual(unfairWager(), 0.5276662759);
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```
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# --seed--
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## --seed-contents--
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```js
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function unfairWager() {
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return true;
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}
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unfairWager();
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```
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# --solutions--
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```js
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// solution required
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```
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