{ "data": { "question": { "questionId": "867", "questionFrontendId": "837", "boundTopicId": null, "title": "New 21 Game", "titleSlug": "new-21-game", "content": "

Alice plays the following game, loosely based on the card game "21".

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Alice starts with 0 points and draws numbers while she has less than k points. During each draw, she gains an integer number of points randomly from the range [1, maxPts], where maxPts is an integer. Each draw is independent and the outcomes have equal probabilities.

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Alice stops drawing numbers when she gets k or more points.

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Return the probability that Alice has n or fewer points.

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Answers within 10-5 of the actual answer are considered accepted.

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Example 1:

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\nInput: n = 10, k = 1, maxPts = 10\nOutput: 1.00000\nExplanation: Alice gets a single card, then stops.\n
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Example 2:

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\nInput: n = 6, k = 1, maxPts = 10\nOutput: 0.60000\nExplanation: Alice gets a single card, then stops.\nIn 6 out of 10 possibilities, she is at or below 6 points.\n
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Example 3:

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\nInput: n = 21, k = 17, maxPts = 10\nOutput: 0.73278\n
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Constraints:

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