400Exam1Aans - Exam 1 1. Suppose P ( A ) = 0.45, (Version A...

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Exam 1 ( Version A – white ) ( Answers ) 1. Suppose P ( A ) = 0.45, P ( B ) = 0.40, P ( C ) = 0.50, P ( A B ) = 0.15, P ( A C ) = 0.20, P ( B C ) = 0.25, P ( A B C ) = 0.05. a) (2) Find P ( A C ) = _______________. b) (3) Find P ( A ( B C ) ) = _______________. c) (5) Find P ( B C | A ' ) = _______________. a) P ( A C ) = P ( A ) + P ( C ) P ( A C ) = 0.45 + 0.50 – 0.20 = 0.75 . b) P ( A ( B C ) ) = 0.65 . c) P ( B C | A ' ) = ( ) ( ) ( ) ' ' A P C B A P = 55 . 0 35 . 0 = 11 7 = 63 0.63 .
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2. Alex sets two alarm clocks each night to ensure that he does not sleep through his 11:00 a.m. class. His primary clock properly sounds its alarm on 90% of the mornings, while his secondary clock rings its bell on only 60% of mornings. Assume the clocks operate independently. a) (3) What percent of the time does Alex’s two-clock strategy prevent him from oversleeping? That is, find the probability that at least one alarm would sound on a given morning. P( 1st OR 2nd ) = P( 1st ) + P( 2nd ) – P( 1st AND 2nd ) = 0.90 + 0.60 – 0.90 × 0.60 = 0.96 . OR P( at least one ) = 1 – P( none ) = 1 – 0.10 × 0.40 = 0.96 . b) (3) Find the probability that only one alarm would sound on a given morning. P( 1st only ) + P( 2nd only ) = 0.90 × 0.40 + 0.10 × 0.60 = 0.42 . 3. (4) In order to create more room in his freezer, Alex took all pizza pockets out of the boxes, but he forgot to label them. He only remembers that 5 are ham and cheese, 7 are pepperoni pizza, and 4 are Philly steak. When a few of his friends drop over for a game of poker, Alex decides to serve pizza pockets. If he selects 5 pockets at random, what is the probability that 2 of them are ham and cheese and 3 are
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This note was uploaded on 02/24/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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400Exam1Aans - Exam 1 1. Suppose P ( A ) = 0.45, (Version A...

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