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Unformatted text preview: Problem Show that b ( n, p, j ) = p q n j + 1 j ¶ b ( n, p, j 1) , for j ≥ 1 . Use this fact to determine the value or values of j which give b ( n, p, j ) its greatest value. 1 Problem Show that the number of ways that one can put n different objects into three boxes with a in the first, b in the second, and c in the third is n ! / ( a ! b ! c !) . 2 Problem Prove that the probability of exactly n heads in 2 n tosses of a fair coin is given by the product of the odd numbers up to 2 n 1 divided by the product of the even numbers up to 2 n . Conditional Probability 10/04/2005 1 Example Three candidates A, B, and C are running for office. We decided that A and B have an equal chance of winning and C is only 1/2 as likely to win as A. Let A be the event “A wins,” B that “B wins,” and C that“C wins.”Hence, we assigned probabilities P ( A ) = 2 / 5 , P ( B ) = 2 / 5 , and P ( C ) = 1 / 5 ....
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This note was uploaded on 07/16/2010 for the course MATH 20 taught by Professor Ionescu during the Fall '05 term at Dartmouth.
 Fall '05
 Ionescu
 Probability

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