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# QUIZ 1-4 - deluxe model or both P W ∪ D = P W P D – P W...

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STAT 400 Spring 2011 Version D Name ANSWERS . Quiz 1 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 40% of the cameras sold have been of the basic model. Of those buying the basic model, 30% purchase an extended warranty, whereas 50% of all deluxe purchasers do so. P( B ) = 0.40. P( W | B ) = 0.30, P( W | D ) = 0.50. a) (4) What proportion of customers purchase an extended warranty over the past year? W W ' B 0.40 0.30 0.12 0.28 0.40 D 0.60 0.50 0.30 0.30 0.60 0.42 0.58 1.00 OR P( W ) = 0.12 + 0.30 = 0.42 .

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OR P( W ) = P( B ) P( W | B ) + P( D ) P( W | D ) = 0.40 0.30 + 0.60 0.50 = 0.42 . b) (2) What proportion of customers either purchase an extended warranty or purchase a
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Unformatted text preview: deluxe model, or both? P( W ∪ D ) = P( W ) + P( D ) – P( W ∩ D ) = 0.42 + 0.60 – 0.30 = 0.72 . OR P( W ∪ D ) = P( W ∩ D ) + P( W ∩ B ) + P( W ' ∩ D ) = 0.30 + 0.12 + 0.30 = 0.72 . OR P( W ∪ D ) = 1 – P( W ' ∩ B ) = 1 – 0.28 = 0.72 . c) (2) If you learn that a randomly selected purchaser has an extended warranty, what is the probability that he/she has a deluxe model? P( D | W ) = 7 5 = = ∩ 42 . 30 . ) W ( P ) W D ( P ≈ 0.7143 . d) (2) Suppose a randomly selected purchaser does not have an extended warranty. What is the probability that he/she has a basic model? P( B | W ' ) = 29 14 = = ∩ 58 . 28 . ) W ( P ) W B ( P ' ' ≈ 0.48276 ....
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QUIZ 1-4 - deluxe model or both P W ∪ D = P W P D – P W...

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