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Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 2 - Problem 25e
Get Full Access to Probability And Statistics For Engineers And The Scientists - 9 Edition - Chapter 2 - Problem 25e

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# The three most popular options on a certain type of new ISBN: 9780321629111 32

## Solution for problem 25E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 25E

The three most popular options on a certain type of new car are a built-in GPS (?A?), a sunroof (?B?), and an automatic transmission (?C?). If 40% of all purchasers request ?A?, 55% request ?B?, 70% request ?C?, 63% request ?A ?or ?B?, 77% request ?A ?or C?, 80% request ?B ?or ?C?, and 85% request ?A ?or ?B ?or ?C?, determine the probabilities of the following events. [?Hint: ?“?A ?or ?B?” is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] a?.? he next purchaser will request at least one of the three options. b?.? he next purchaser will select none of the three options. c?. ?The next purchaser will request only an automatic transmission and not either of the other two options. d?.? he next purchaser will select exactly one of these three options.

Step-by-Step Solution:
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Problem 25E Answer: Step1: We have The three most popular options on a certain type of new car are a built-in GPS (A), a sunroof (B), and an automatic transmission (C). If 40% of all purchasers request A, 55% request B, 70% request C, 63% request A or B, 77% request A or C, 80% request B or C, and 85% request A or B or C, determine the probabilities of the following events. [Hint: “A or B” is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] That is P(A) = 0.40 P(B) = 0.55 P(C) = 0.70 P(AB) = 0.63 P(AC) = 0.77 P(BC) = 0.80 P(ABC) = 0.85 Our goal is to find, a. The next purchaser will request at least one of the three options. b. The next purchaser will select none of the three options. c. The next purchaser will request only an automatic transmission and not either of the other two options. d. The next purchaser will select exactly one of these three options. Step2: a). The probability that the next purchaser will select at least one of the three options is determined with the following equations P(ABC) = P(A) + P(B) + P(C) –P(AB) – P(AC) – P(BC) + P(ABC) Where, P(AB) = P(A) + P(B) - P(AB) = 0.40 + 0.55 - 0.63 = 0.32 P(AC) = P(A) + P(C) – P(AC) = 0.40 + 0.70 - 0.77 = 0.33 P(BC) = P(B) + P(C) – P(BC) = 0.55 + 0.70 - 0.80 = 0.45 P(ABC) = -P(A) – P(B) – P(C) + P(AB) + P(AC) + P(BC) + P(ABC) = -0.40 - 0.55 - 0.70 + 0.32 + 0.33 + 0.45 + 0.85 = 0.30 The next purchaser will request at least one of the three options is P(ABC) = 0.85. Step3: b). The next purchaser will select none of the three options is given by ( ) = 1 P( ) = 1 P ( ) = 1 - 0.85 = 0.15 Therefore, ( ) = 0.15. Step4: c). The next purchaser will request only an automatic transmission and not either of the other two options is given by ( ) = P(ABC) - P(AB) = 0.85 - 0.63 = 0.22 Step5: d). The next purchaser will select exactly one of these three options is given by ( ) = 0.05 +0.08 +0.22 = 0.35 Therefore, ( ) = 0.35.

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##### ISBN: 9780321629111

The full step-by-step solution to problem: 25E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Since the solution to 25E from 2 chapter was answered, more than 1814 students have viewed the full step-by-step answer. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. This full solution covers the following key subjects: request, options, next, purchaser, automatic. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. The answer to “The three most popular options on a certain type of new car are a built-in GPS (?A?), a sunroof (?B?), and an automatic transmission (?C?). If 40% of all purchasers request ?A?, 55% request ?B?, 70% request ?C?, 63% request ?A ?or ?B?, 77% request ?A ?or C?, 80% request ?B ?or ?C?, and 85% request ?A ?or ?B ?or ?C?, determine the probabilities of the following events. [?Hint: ?“?A ?or ?B?” is the event that at least one of the two options is requested; try drawing a Venn diagram and labeling all regions.] a?.? he next purchaser will request at least one of the three options. b?.? he next purchaser will select none of the three options. c?. ?The next purchaser will request only an automatic transmission and not either of the other two options. d?.? he next purchaser will select exactly one of these three options.” is broken down into a number of easy to follow steps, and 148 words.

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