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# HW1S - ISE 220 PROBABILITY CONCEPTS IN ENGINEERING...

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ISE 220 PROBABILITY CONCEPTS IN ENGINEERING Solutions to Homework Problem Set # 1 Instructor: Dr. Ashok Patel Fall 2010 Problem 1 a) B C c b) A D E c c) A B c C D c d) A c C e) C D f) (B C) (A c C c ) Problem 2 a) {5, 7} b) {6, 8} c) C = {0, 1, 2, 4, 6, 8, 10} d) {5, 7} e) {0, 2, 4, 5, 6, 7, 8, 10} f) {3,5,6,7,8,9} g) φ h) {3, 9} Problem 3 glyph1197ote : “Both Train and Bus arrives at the same time” “the bus and the train meet” but “Both Train and Bus arrives at the same time” “the bus and the train meet”

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Problem 4 (a) S 1 = { HHH, HHT, HTH, HTT, THH, THT, TTH, TTT }. (b) S 2 = { 0, 1, 2, 3 } and following are the all possible 16 subsets of S 2 : φ , S 2 , {0}, {1}, {2}, {3}, {0,1}, {0,2}, {0,3}, {1,2}, {1,3}, {2,3}, {0,1,2}, {0,1,3}, {0,2,3}, {0,3,1}. Q : When does a subset of a sample space represent some event? Ans : Suppose that a subset A describes (or represents) some event E. Then this event E must occur whenever any outcome from the set A occurs, and vice versa. E 1 = more than two heads (i.e. Heads on all three tosses).
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