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# chap-2 - Chapter 2 Problems 1 2(a S =(r r(r g(r b(g r(g g(g...

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10 Chapter 2 Chapter 2 Problems 1. (a) S = {( r , r ), ( r , g ), ( r , b ), ( g , r ), ( g , g ), ( g , b ), ( b , r ), b , g ), ( b , b )} (b) S = {( r , g ), ( r , b ), ( g , r ), ( g , b ), ( b , r ), ( b , g )} 2. S = {( n , x 1 , …, x n 1 ), n 1, x i 6, i = 1, …, n 1}, with the interpretation that the outcome is ( n , x 1 , …, x n 1 ) if the first 6 appears on roll n , and x i appears on roll, i , i = 1, …, n 1. The event c n n E ) ( 1 = is the event that 6 never appears. 3. EF = {(1, 2), (1, 4), (1, 6), (2, 1), (4, 1), (6, 1)}. E F occurs if the sum is odd or if at least one of the dice lands on 1. FG = {(1, 4), (4, 1)}. EF c is the event that neither of the dice lands on 1 and the sum is odd. EFG = FG . 4. A = {1,0001,0000001, …} B = {01, 00001, 00000001, …} ( A B ) c = {00000 …, 001, 000001, …} 5. (a) 2 5 = 32 (b) W = {(1, 1, 1, 1, 1), (1, 1, 1, 1, 0), (1, 1, 1, 0, 1), (1, 1, 0, 1, 1), (1, 1, 1, 0, 0), (1, 1, 0, 1, 0) (1, 1, 0, 0, 1), (1, 1, 0, 0, 0), (1, 0, 1, 1, 1), (0, 1, 1, 1, 1), (1, 0, 1, 1, 0), (0, 1, 1, 1, 0), (0, 0, 1, 1, 1) (0, 0, 1, 1, 0), (1, 0, 1, 0, 1)} (c) 8 (d) AW = {(1, 1, 1, 0, 0), (1, 1, 0, 0, 0)} 6. (a) S = {(1, g ), (0, g ), (1, f ), (0, f ), (1, s ), (0, s )} (b) A = {(1, s ), (0, s )} (c) B = {(0, g ), (0, f ), (0, s )} (d) {(1, s ), (0, s ), (1, g ), (1, f )} 7. (a) 6 15 (b) 6 15 3 15 (c) 4 15 8. (a) .8 (b) .3 (c) 0 9. Choose a customer at random. Let A denote the event that this customer carries an American Express card and V the event that he or she carries a VISA card. P ( A V ) = P ( A ) + P ( V ) P ( AV ) = .24 + .61 .11 = .74. Therefore, 74 percent of the establishment’s customers carry at least one of the two types of credit cards that it accepts.

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Chapter 2 11 10. Let R and N denote the events, respectively, that the student wears a ring and wears a necklace. (a) P ( R N ) = 1 .6 = .4 (b) .4 = P ( R N ) = P ( R ) + P ( N ) P ( RN ) = .2 + .3 P ( RN ) Thus, P ( RN ) = .1 11. Let A be the event that a randomly chosen person is a cigarette smoker and let B be the event that she or he is a cigar smoker. (a) 1 P ( A B ) = 1 (.07 + .28 .05) = .7. Hence, 70 percent smoke neither. (b) P ( A c B ) = P ( B ) P ( AB ) = .07 .05 = .02. Hence, 2 percent smoke cigars but not cigarettes. 12. (a) P ( S F G ) = (28 + 26 + 16 12 4 6 + 2)/100 = 1/2 The desired probability is 1 1/2 = 1/2. (b) Use the Venn diagram below to obtain the answer 32/100. 14 10 10 S F 8 G 2 4 2 (c) since 50 students are not taking any of the courses, the probability that neither one is taking a course is 2 100 2 50 = 49/198 and so the probability that at least one is taking a course is 149/198. 13. (a) 20,000 (b) 12,000 (c) 11,000 (d) 68,000 (e) 10,000 1000 7000 19000 I II 0 III 1000 3000 1000
12 Chapter 2 14. P ( M ) + P ( W ) + P ( G ) P ( MW ) P ( MG ) P ( WG ) + P ( MWG ) = .312 + .470 + .525 .086 .042 .147 + .025 = 1.057 15. (a) 5 52 5 13 4 (b) 5 52 1 4 1 4 1 4 3 12 2 4 13 (c) 5 52 1 44 2 4 2 4 2 13 (d) 5 52 1 4 1 4 2 12 3 4 13 (e)

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