winter 2006 s230_test1B_solutions

winter 2006 s230_test1B_solutions - STAT 230 Test #1 Jan...

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STAT 230 Test # 1 Jan 18 , 2006 3 : 30 4 : 15 p . m . Name : SI . D : UWUserid : Mark / 25 Circle your instructor and time slot : 1 . McLeish ( 10 : 30 ) 2 . Zhu ( 12 : 30 ) 3 . Drekic ( 1 : 30 ) [ 10 ] 1 . The digits 1,2, ,6 are randomly arranged in a row. a . What is the sample space? S {All permutations of (1,2,3,4,5,6)} {(1,2,3,4,5,6), , (6,5,4,3,2,1)}. In particular, notice that the number of points in S is 6!.(please note: the sample space is a set–a set is not the same as the number of points in it) b . Find the probability that the first digit is 1 and last digit is 6. (Show your work!) Positions 1 and 6 are fixed; the middle four can permute. Answer 1 4! 1 /6!. c . Find the probability that all three even numbers occur consecutively (i.e. side by side in any order). (Show your work!) Sol n1 : denote the three even numbers by the symbol E . There are 4! permuations of the symbols 135 E and for each of these there are 3! ways of permuting the even numbers within
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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 s230_test1B_solutions - STAT 230 Test #1 Jan...

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