hwmk2sol

# hwmk2sol - Solutions to Homework 2 ISyE 2027 Fall 2006...

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Solutions to Homework 2, ISyE 2027 Fall 2006 Problem 1 (a) Let A = { H, T } (where H denotes heads and T represents tails), and let B = { 1 , 2 , 3 , 4 , 5 , 6 } . A reasonable sample space S is A × B , where A × B := { ( i, j ) : i A, j B } . (b) There are (2)(6) = 12 outcomes in S . (c) If the die and coin are fair, then the outcomes are equally likely. Problem 2 (a) P ( A ) = 1 - P ( A ) = 1 - . 4 = . 6. (b) P ( A B ) = P ( A ) + P ( B ) - P ( A B ) = . 4 + . 3 - . 1 = . 6. (c) DeMorgan’s law tells us that A B = A B , so P ( A B ) = P ( A B ) = 1 - P ( A B ) = 1 - . 6 = . 4 . (d) P ( A B ) = P ( A ) + P ( B ) - P ( A B ) = . 6 + . 7 - . 4 = . 9. (e) A and B are not disjoint, since P ( A B ) = . 1 > 0. Recall that two sets are disjoint if A B = . We also know that P ( ) = 0, which excludes the possibility of A and B being disjoint. Problem 3

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hwmk2sol - Solutions to Homework 2 ISyE 2027 Fall 2006...

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