51 lines
1.1 KiB
Markdown
51 lines
1.1 KiB
Markdown
---
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id: 5900f4551000cf542c50ff67
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title: 'Problem 232: The Race'
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challengeType: 5
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forumTopicId: 301876
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dashedName: problem-232-the-race
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---
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# --description--
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Two players share an unbiased coin and take it in turns to play "The Race".
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On Player 1's turn, he tosses the coin once: if it comes up Heads, he scores one point; if it comes up Tails, he scores nothing.
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On Player 2's turn, she chooses a positive integer $T$ and tosses the coin $T$ times: if it comes up all Heads, she scores $2^{T - 1}$ points; otherwise, she scores nothing.
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Player 1 goes first. The winner is the first to 100 or more points.
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On each turn Player 2 selects the number, $T$, of coin tosses that maximises the probability of her winning.
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What is the probability that Player 2 wins?
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Give your answer rounded to eight decimal places in the form 0.abcdefgh .
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# --hints--
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`theRace()` should return `0.83648556`.
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```js
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assert.strictEqual(theRace(), 0.83648556);
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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 theRace() {
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return true;
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}
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theRace();
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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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