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Unformatted text preview: , i = 1 ,...k, to be the event that the ith member of the ﬁxed set picks her/his own hat. Then, describing event E in terms of the G i , i = 1 ,...k , we have that P ( E ) = = , using the multiplication rule, = , evaluating each term, = . 3. Next, we want to calculate P ( F  E ), or in words, P ( F  E ) = P ( ) = , using ( * ), since the remaining ( Nk ) graduates are choosing from among their own ( Nk ) hats. 4. So, for the ﬁxed set of k graduates, the probability that we wish to calculate is P ( EF ) = . 5. Accounting for the number of ways we could have chosen the ﬁxed set of k graduates, this gives us the overall answer of P (exactly k matches) = , = ....
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This note was uploaded on 10/14/2010 for the course MATH 319 taught by Professor Clionagolden during the Spring '10 term at Bard College.
 Spring '10
 ClionaGolden
 Math, Statistics, Probability

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