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set1solutions - IE 300 / GE 331 Discussion Problem Set 1...

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IE 300 / GE 331 Discussion Problem Set 1 2-17 (Sample space and events) Describe both the sample space and the event “ at most four calls are needed to get connected” c = connected, b = busy, S = {c, bc, bbc, bbbc, bbbbc, …}, E={c, bc, bbc, bbbc} 2-19 (e) (Venn diagram) (Event operations) The sample space of a random experiment is S={1,2,3,. ..,10} . Three events A, B and C are such that A B={3,4,5}, A U B={1,2,3,4,5}, C={4,5,6}. What are A U B ’, A B and (A C) U (B C) ? By DeMorgan’s laws, }, 10 , 9 , 8 , 7 , 6 , 2 , 1 { )' ( ' ' = = B A B A I U }. 10 , 9 , 8 , 7 , 6 { )' ( ' ' = = B A B A U I By Distributive law, ( 29 ( 29 ( 29 {1,2,3,4,5} {4,5,6} {4,5} A C B C A B C = = = I U I U I I 2-42 (Counting) a) If the chips are of different types, then every arrangement of 5 locations selected from the 12 results in a different layout. Therefore, 040 , 95 ! 7 ! 12 12 5 = = P layouts are possible. b)
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set1solutions - IE 300 / GE 331 Discussion Problem Set 1...

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