55 lines
1.5 KiB
Markdown
55 lines
1.5 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". 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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`euler436()` should return 0.5276662759.
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```js
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assert.strictEqual(euler436(), 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 euler436() {
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return true;
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}
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euler436();
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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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