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2008 1 - Stat 230 Spring 2008 STAT 230 Spring 2008 Test 1...

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Stat 230 Spring 2008 STAT 230 - Spring 2008 - Test 1 SOLUTIONS 1. [8 marks] A 5-digit number is created by randomly selecting the digits { 2 , 3 , 4 , 5 , 6 , 7 , 8 } without replacement . Find the probability of the following events. (a) [2 marks] The randomly created number is odd. Number of possible numbers: 7 (5) = 2520 Number of odd numbers: 3 6 (4) = 1080 So P(odd) = 1080 / 2520 = 3 / 7 = 0 . 4286. (b) [3 marks] The pattern 237 appears. It can appear as 237xx, x237x, or xx237. Each has 4 (2) = 12 ways to fill the remaining digits So there are 3 12 = 36 ways for it to occur. So P(”237”) = 36 / 2520 = 1 / 70 = 0 . 0143. (c) [3 marks] The numbers { 2 , 3 , 7 } appear together in any order. Using the same cases in (b), each pattern can now occur 3! times. So there are 3 12 3! = 216 ways for it to occur. So P(2,3,7) = 216 / 2520 = 3 / 35 = 0 . 0857.
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Stat 230 Spring 2008 2. [10 marks] Two boys and two girls randomly select one of five sections of STAT 230. Find the probability of the following events. (a) [2 marks] All four students pick the same section. Number of ways for students to choose sections: 5 4 = 625.
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