ORIE 360/560 Fall 2007
Due Tuesday, Sept. 11 at 2:00 pm
A traveler puts her passport in one of
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
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
drawers, where 0
(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?
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