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# hw02 - ORIE 360/560 Fall 2007 Assignment 2 Due Tuesday Sept...

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ORIE 360/560 Fall 2007 Assignment 2 Due Tuesday, Sept. 11 at 2:00 pm Problem 1. A traveler puts her passport in one of n drawers in her desk, but has forgotten which one. Before starting a journey, she is frantically looking for it. She tries the drawers in a random order, without repitition. But, due to nervous haste, with probability p she does not notice the passport even if she opens the drawer containing it. (a) What is the probability that she will fail to ﬁnd her passport after opening k drawers, where 0 k n ? (b) Suppose she has opened k < n drawers and not yet found the passport. What is the conditional probability that she has not yet opened the drawer containing the passport? Problem 2. a) A poker deck consists of cards ranked 2,3,4,5,6,7,8,9,10,J,Q,K,A, (13 diﬀerent ranks) each in four suits, for a total of 52 distinct cards. What is the probability that a ﬁve-card poker hand drawn from a poker deck consists only of cards ranked 9,10,J,Q,K,A? b) A pinochle deck consists of
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