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HW1Answers(1.2) - Math331 Spring 2008 Instructor David...

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Math331, Spring 2008 Instructor: David Anderson Section 1.1 and 1.2 Hw answers Homework: pgs. 9 - 11, #’s 2, 3, 5, 9, 13, 17(a) 2. The sample space is given by S = { ( i,j,k ) | i,j,k ∈ { red,blue }} . 3. The sample space is S = { t : t (0 , 20) } . The event that the number is an integer is E = { 1 , 2 , 3 ,..., 19 } . 5. E is the event that the sum is odd. F is the event that at least one 1 is rolled. E F implies one 1 and one even number (so the sum is odd). E c F implies one 1 and one odd number (so the sum is even). E c F c implies the sum is even and neither was a 1. Thus, both even or both in { 3 , 5 } . 9. Let a i b j be the event that passenger a gets off at hotel i and likewise for b . Here i,j ∈ { 1 , 2 , 3 } . Then S = { a i b j : i,j ∈ { 1 , 2 , 3 }} . Alternatively (there is no unique answer here) S = { ( i,j ) : i,j ∈ { 1 , 2 , 3 }} , where the first element of ( · , · ) represents the number of the hotel (1,2, or 3) that passenger A gets off at and the second element represents the number of the hotel for passenger B . The event that both get off at the same hotel is { (1 , 1) , (2 , 2) , (3 , 3) } . 13. (a) E - E F = E ( E F ) c = E ( E c F c ) = ( E E c ) ( E F c ) = E F c . Thus, ( E - E F ) F = ( E F c ) F = ( E F ) ( F c F ) = ( E
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