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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 ﬁvecard 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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 Fall '07
 EHRLICHMAN

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