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Unformatted text preview: STA 4321 Solution to Homework 1 2.10 a . Because the two jobs are indentical, the order is not important in this problem. The sample space is S = {{ J,D } , { J,M } , { J,S } , { J,N } , { D,M } , { D,S } , { D,N } , { M,S } , { M,N } , { S,N }} . Each person is denoted by the first letter of her/his name. b . At least one of Jim and Don should be selected, so A = {{ J,D } , { J,M } , { J,S } , { J,N } , { D,M } , { D,S } , { D,N }} . There are 7 outcomes in A . c . Exactly one in Jim and Don is selected, so B = {{ J,M } , { J,S } , { J,N } , { D,M } , { D,S } , { D,N }} . There are 6 outcomes in B . d . Let C denote the event that two males are selected. Then C = {{ J,D }} = A ∩ B. e . A = {{ M,S } , { M,N } , { S,N }} . A ∩ B = {{ J,M } , { J,S } , { J,N } , { D,M } , { D,S } , { D,N }} . A ∪ B = {{ J,D } , { J,M } , { J,S } , { J,N } , { D,M } , { D,S } , { D,N } , { M,S } , { M,N } , { S,N }} . A ∩ B = {{ J,D } , { M,S } , { M,N } , { S,N }} . 2.12 Let A denote the event that the selected student has drunk alcohol during the past month, B denote the event that the selected student has used a tobacco product during the past month. Then P( A )=0.84, P( B )=0.33, and P( A ∪ B )=0.86. a . P( A ∩ B )=P( A )+P( B )P( A ∪ B )=0.84+0.330.86=0.31. b . P( A ∪ B )=1P( A ∪ B )=10.86=0.14. c . P(( A ∪ B ) ∩ ( A ∩ B ))=P( A ∪ B )P( A ∩ B )=0.860.31=0.75. (The first equation holds because ( A ∪ B ) ∩ ( A ∩ B ) and A ∩ B are mutually exclusive.) 2.13 Let A denote the event the selected student reads the school newspaper,...
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This note was uploaded on 12/15/2011 for the course STA 4321 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
 Staff
 Probability

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