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hw2solu_427

# hw2solu_427 - HW 2 Solutions All from Chapter 2 45 a b P(A...

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HW 2 Solutions: All from Chapter 2 45. a. P(A) = .106 + .141 + .200 = .447, P(C) =.215 + .200 + .065 + .020 = .500 P(A C) = .200 b. P(A|C) = 400 . 500 . 200 . ) ( ) ( C P C A P . If we know that the individual came from ethnic group 3, the probability that he has type A blood is .40. P(C|A) = 447 . 447 . 200 . ) ( ) ( A P C A P . If a person has type A blood, the probability that he is from ethnic group 3 is .447 c. Define event D = {ethnic group 1 selected}. We are asked for P(D|B ) = 211 . 909 . 192 . ) ( ) ( B P B D P . P(D B )=.082 + .106 + .004 = .192, P(B ) = 1 P(B) = 1 [.008 + .018 + .065] = .909 48. a. P(A 2 A 1 ) = 50 . 12 . 06 . ) ( ) ( 1 2 1 A P A A P b. P(A 1 A 2 A 3 A 1 ) = 0833 . 12 . 01 . c. We want P[(exactly one) (at least one)]. P(at least one) = P(A 1 A 2 A 3 ) a. = .12 + .07 + .05 .06 .03 .02 + .01 = .14 Also notice that the intersection of the two events is just the 1 st event, since “exactly one” is totally contained in “at least one.” So P[(exactly one) (at least one)]= 3571 . 14 . 01 . 04 . d. The pieces of this equation can be found in your answers to exercise 26 (section 2.2): 833 .

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