A sultan has given an aam aadmi a choice to marry one of his 100 daghters. The commoner will be presented with the daughters one at a time and, when each daughter is presented, the commoner will be told the daughter's dowry (which is fixed in advance). Upon being presented with a daughter, the commoner must immediately decide whether to accept or reject her (he is not allowed to return to a previously rejected daughter). However, the sultan will allow the marriage to take place only if the commoner picks the daughter with the overall highest dowry. Then what is the commoner's best strategy, assuming he knows nothing about the distribution of dowries ??
sultan kee beti kee shaadi
- Thread starter mbamal
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Since the commoner knows nothing about the distribution of the dowries, the best strategy is to wait until a certain number of daughters have been presented then pick the highest dowry thereafter. The exact number to skip is determined by the condition that the odds that the highest dowry has already been seen is just greater than the odds that it remains to be seen AND THAT IF IT IS SEEN IT WILL BE PICKED. This amounts to finding the smallest x such that:
x/n > x/n * (1/(x+1) + ... + 1/n).
Working out the math for n=100 and calculating the probability gives: The commoner should wait until he has seen 37 of the daughters, then pick the first daughter with a dowry that is bigger than any preceding dowry. With this strategy, his odds of choosing the daughter with the highest dowry are surprisingly high: about 37%
x/n > x/n * (1/(x+1) + ... + 1/n).
Working out the math for n=100 and calculating the probability gives: The commoner should wait until he has seen 37 of the daughters, then pick the first daughter with a dowry that is bigger than any preceding dowry. With this strategy, his odds of choosing the daughter with the highest dowry are surprisingly high: about 37%
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