Stat 5131 (Geyer) First Midterm Solutions

# Stat 5131 (Geyer) First Midterm Solutions - Up Stat 5131...

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Up: Stat 5131 Stat 5131 (Geyer) Midterm 1 Problem 1 This is solved using a two-stage 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 4-3-3-3 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 ).

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