Asst2-solved

Asst2-solved - Statistics 427: Homework #2 Solutions to...

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Statistics 427: Homework #2 Solutions to Assigned Problems 2.45 [10 pts (3,4,3)] (a) P ( A ) = 0 . 106 + 0 . 141 + 0 . 200 = 0 . 447 P ( C ) = 0 . 215 + 0 . 200 + 0 . 065 + 0 . 020 = 0 . 5 P ( A C ) = 0 . 200 (b) P ( A | C ) = P ( A C ) P ( C ) = 0 . 200 0 . 5 = 0 . 4 P ( C | A ) = P ( C A ) P ( A ) = 0 . 200 0 . 447 = 0 . 44742 P ( A | C ) represents the probability that someone from ethnic group 3 has blood type A. P ( C | A ) represents the probability that a person with blood type A is from ethnic group 3. (c) Let D = { ethnic group 1 selected } . P ( D | B 0 ) = P ( D B 0 ) P ( B 0 ) . Now P ( B ) = 0 . 008 + 0 . 018 + 0 . 065 = 0 . 091 and so P ( B 0 ) = 1 - 0 . 091 = 0 . 909. So P ( D | B 0 ) = P ( D B 0 ) P ( B 0 ) = 0 . 082 + 0 . 106 + 0 . 004 0 . 909 = 0 . 192 0 . 909 = 0 . 211 . 2.47 [10 pts (2,2,2,2,2)] (a) We know P ( A ) = 0 . 5, P ( B ) = 0 . 4, and P ( A B ) = 0 . 25. So P ( B | A ) = P ( A B ) P ( A ) = 0 . 25 0 . 5 = 0 . 5 . This means that 50% of Visa card holders have a MasterCard.
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Asst2-solved - Statistics 427: Homework #2 Solutions to...

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