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5934概率中等数值题medium

Sultan's Dowry with Five Suitors

题目

A sultan offers a vizier the hand of one of 5 daughters, presented one at a time in uniformly random order. After meeting a daughter, the vizier learns only how she ranks (by dowry) relative to those already seen and must immediately and irrevocably accept or send her away; if he reaches the last he must take her. He wins only by choosing the single highest dowry. Among all 'skip the first r, then take the first daughter who beats every earlier one' rules, find the optimal r and the exact probability of winning.

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