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Homework1

# Homework1 - HOMEWORK PROBLEMS#1 SOLUTIONS TO EVEN PROBLEMS...

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HOMEWORK PROBLEMS #1 SOLUTIONS TO EVEN PROBLEMS 2. (a) A B (b) A B (c) A B = A B (d) There are many ways of denoting this, here are a couple: ( A B ) - ( A B ) = ( A B ) ( A B ) 4. (a) & . (b) & . 1

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2 SOLUTIONS TO EVEN PROBLEMS 6. (a) A = { ( x, y ) | x = 1 , 2 , 3 , 4 , 5 , 6 and y = 2 , 4 , 6 } , B = { ( x, y ) | x = 1 , 2 , 3 , 4 , 5 , 6 and y = 1 , 2 , 3 , 4 , 5 , 6 and x + y is even } , C = { ( x, y ) | x = 1 , 2 , 3 , 4 , 5 , 6 and y = 1 , 2 , 3 , 4 , 5 , 6 and x or y is odd } (b) A = { (1 , 2) , (2 , 2) , (3 , 2) , (4 , 2) , (5 , 2) , (6 , 2) , (1 , 4) , (2 , 4) , (3 , 4) , (4 , 4) , (5 , 4) , (6 , 4) , (1 , 6) , (2 , 6) , (3 , 6) , (4 , 6) , (5 , 6) , (6 , 6) } , C = { (2 , 2) , (2 , 4) , (2 , 6) , (4 , 2) , (4 , 4) , (4 , 6) , (6 , 2) , (6 , 4) , (6 , 6) } , A B = C = { (2 , 2) , (2 , 4) , (2 , 6) , (4 , 2) , (4 , 4) , (4 , 6) , (6 , 2) , (6 , 4) , (6 , 6) } , A B = { (1 , 2) , (1 , 4) , (1 , 6) , (3 , 2) , (3 , 4) , (3 , 6) , (5 , 2) , (5 , 4) , (5 , 6) } , A B = { (1 , 1) , (2 , 1) , (3 , 1) , (4 , 1) , (5 , 1) , (6 , 1) , (1 , 3) , (2 , 3) , (3 , 3) , (4 , 3) , (5 , 3) , (6 , 3) , (1 , 5) , (2 , 5) , (3 , 5) , (4 , 5) , (5 , 5) , (6 , 5) , (2 , 2) , (4 , 2) , (6 , 2) , (2 , 4) , (4 , 4) , (6 , 4) , (2 , 6) , (4 , 6) , (6 , 6) } , A C = A = { (1 , 1) , (2 , 1) , (3 , 1) , (4 , 1) , (5 , 1) , (6 , 1) , (1 , 3) , (2 , 3) , (3 , 3) , (4 , 3) , (5 , 3) , (6 , 3) , (1 , 5) , (2 , 5) , (3 , 5) , (4 , 5) , (5 , 5) , (6 , 5) } . 14. (a) . 44 + . 14 = . 58 (b) . 14 (c) . 44 + . 02 = . 46 18. (a) S = { HH, HT, TH, TT } (b) The sample points should be equally likely, because we are told that the coins are balanced, so P ( HH ) = P ( HT ) = P ( TH ) = P ( TT ) = 1 4 . (c) A = { HT, TH } , B = { HH, HT, TH } . (d) P ( A ) = P ( HT ) + P ( TH ) = 1 4 + 1 4 = 1 2 , P ( B ) = P ( HH ) + P
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Homework1 - HOMEWORK PROBLEMS#1 SOLUTIONS TO EVEN PROBLEMS...

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