winter 2006 s230_test1_solutions

Winter 2006 - STAT 230 Test#1 3:30 4:15 pm UWUserid Name I.D Circle your instructor and time slot 1 McLeish(10:30 2 Zhu(12:30 3 Drekic(1:30 1 The

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STAT 230 Test # 1 Jan 18 , 2006 3 : 30 4 : 15 pm Name : I . D : UWUserid : Circle your instructor and time slot : 1 . McLeish ( 10 : 30 ) 2 . Zhu ( 12 : 30 ) 3 . Drekic ( 1 : 30 ) 1 . The digits 1,2, ,5 are randomly arranged in a row. a . What is the sample space? S {All permutations of (1,2,3,4,5)} {(1,2,3,4,5), , (5,4,3,2,1)}. In particular, notice that the number of points in S is 5!. b . Find the probability that the first digit is 1 and last digit is 5. (Show your work!) Positions 1 and 5 are fixed; the middle three can permute. Answer (1x3!x1)/5! 1/20. c . Find the probability that the even numbers occur consecutively (i.e. side by side). (Show your work!) Sol n1 : denote the two even numbers by E. There are 4! permuations of the symbols 135 E and for each of these there are 2 ways of permuting the even numbers 24 within E . Hence 2 4! 5!
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This note was uploaded on 03/03/2010 for the course STAT 230 taught by Professor Various during the Winter '06 term at Waterloo.

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Winter 2006 - STAT 230 Test#1 3:30 4:15 pm UWUserid Name I.D Circle your instructor and time slot 1 McLeish(10:30 2 Zhu(12:30 3 Drekic(1:30 1 The

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