HW1soln - OR 3500/5500, Summer'08, Homework 1 Homework 1...

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OR 3500/5500, Summer’08, Homework 1 Homework 1 Due on Tuesday, May 27, 11am. For each problem just giving the answer will not suffice; a proper argument is required. Problem 1 A fair die is rolled twice. (a) List the elements in the following events: A =At least one of the rolls is 6. B =The sum of the rolls is 8. C =Product of the two rolls is divisible by 6. (b) Compute P ( A ), P ( B ) and P ( C ) using the classical definition of probability. Solution (a) A = { (1 , 6) , (2 , 6) , (3 , 6) , (4 , 6) , (5 , 6) , (6 , 1) , (6 , 2) , (6 , 3) , (6 , 4) , (6 , 5) , (6 , 6) } B = { (2 , 6) , (3 , 5) , (4 , 4) , (5 , 3) , (6 , 2) } C = { (1 , 6) , (2 , 3) , (2 , 6) , (3 , 2) , (3 , 4) , (3 , 6) , (4 , 3) , (4 , 6) , (5 , 6) , (6 , 1) , (6 , 2) , (6 , 3) , (6 , 4) , (6 , 5) , (6 , 6) } (b)Sample space is: Ω = { ( i,j ) : 1 i,j 6 } Clearly #Ω = 36 and hence P ( A ) = 11 / 36 P ( B ) = 5 / 36 P ( C ) = 5 / 12 Problem 2 Prove rigorously, using the axioms and derived properties of probability
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This note was uploaded on 06/15/2008 for the course ORIE 360 taught by Professor Ehrlichman during the Summer '07 term at Cornell University (Engineering School).

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HW1soln - OR 3500/5500, Summer'08, Homework 1 Homework 1...

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