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Stat 5131
Stat 5131 (Geyer) Midterm 1
Problem 1
This is solved using a twostage process exactly like we used to calculate the probability of most of the
poker hands (full house, three of a kind, two pair, one pair). First we choose which suit gets the four
cards. There are
ways to do that. The other three suits get three cards, there is no choice
remaining about how many cards go to which suit. Second we choose which cards go to each suit. There
are
ways to choose cards for the suit that gets four cards and
ways to choose cards for the other
three suits. Thus there are
bridge hands with 4333 distribution. Since there are
possible bridge hands, the answer is
(The numerical answer is not necessary for full credit, just the formula).
Problem 2
This is a Bayes rule problem. Let
A
denote the event that the computer has an Acme disk, let
B
denote the
event that the computer has a Barfulous disk, and
F
denote the event that the disk fails. Then we are given
in the problem statement
We are asked to calculate
P
(
A

F
).
Bayes rule is
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 Spring '02
 Staff
 Probability

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