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Math Help - Probability-Computer Science problem

  1. #1
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    Probability-Computer Science problem

    The nation is being bombed. The army builds a grid of identical looking houses to camouflage their head-quarters which was meant to be one of them. Yet, the enemy spy network being very efficient gets this information that the headquarters lie among the houses.

    The grid can be visualized as an mxn array.

    There is one house in each grid location. Now, during the war, one of the enemy tanks was able to reach near the houses. It then started bombarding the houses in a random way, with each house having equal probability of getting hit. Assuming that no house gets demolished in any number of hits, one bomb hits only one house, and none of the bombs go disarray, what is the expected number of bombardments in which the enemy would have hit all houses at least once?

    The army needs to know this number as it has to act before this happens.
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  2. #2
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    Quote Originally Posted by p vs np View Post
    The nation is being bombed. The army builds a grid of identical looking houses to camouflage their head-quarters which was meant to be one of them. Yet, the enemy spy network being very efficient gets this information that the headquarters lie among the houses.

    The grid can be visualized as an mxn array.

    There is one house in each grid location. Now, during the war, one of the enemy tanks was able to reach near the houses. It then started bombarding the houses in a random way, with each house having equal probability of getting hit. Assuming that no house gets demolished in any number of hits, one bomb hits only one house, and none of the bombs go disarray, what is the expected number of bombardments in which the enemy would have hit all houses at least once?

    The army needs to know this number as it has to act before this happens.
    Hi p-np,

    This is a disguised version of the "Coupon Collector's Problem": see
    Coupon collector's problem - Wikipedia, the free encyclopedia.

    The houses correspond to coupons; hitting all the houses at least once corresponds to getting a complete set of coupons.
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