14 lines
886 B
Markdown
14 lines
886 B
Markdown
You have two soups, A and B, each starting with n mL. On every turn, one of the following four serving operations is chosen at random, each with probability 0.25 independent of all previous turns:
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pour 100 mL from type A and 0 mL from type B
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pour 75 mL from type A and 25 mL from type B
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pour 50 mL from type A and 50 mL from type B
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pour 25 mL from type A and 75 mL from type B
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Note:
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There is no operation that pours 0 mL from A and 100 mL from B.
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The amounts from A and B are poured simultaneously during the turn.
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If an operation asks you to pour more than you have left of a soup, pour all that remains of that soup.
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The process stops immediately after any turn in which one of the soups is used up.
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Return the probability that A is used up before B, plus half the probability that both soups are used up in the same turn. Answers within 10-5 of the actual answer will be accepted. |