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Ch 2 - 47E

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 47E Chapter 2

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

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

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

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Problem 47E

47E

Step-by-Step Solution:
Step 1 of 3

Problem 47E Answer: Step1: We have Return to the credit card scenario of Exercise 12 (Section 2.2), and let C be the event that the selected student has an American Express card. In addition to P(A) = 0.6, P(B) = 0.4, and P(A B) = 0.3, P(C) = 0.2, P(A C) = 0.15, P(B C) = 0.1, and P(A B C) = 0.08. Our goal is to find, a. What is the probability that the selected student has at least one of the three types of cards b. What is the probability that the selected student has both a Visa card and a MasterCard but not an American Express card c. Calculate and interpret P(B | A) and also P(A | B). d. If we learn that the selected student has an American Express card, what is the probability that she or he also has both a Visa card and a MasterCard e. Given that the selected student has an American Express card, what is the probability that she or he has at least one of the other two types of cards Step2: a). The probability that the selected student has at least one of the three types of cards is given by P(ABC) = P(A)+P(B)+P(C)-P(AB)-P(BC)-P(AC)+P (A B C) = 0.6 + 0.4 + 0.2 - 0.3 - 0.1 - 0.15 + 0.08 = 0.73 b). the probability that the selected student has both a Visa card and a MasterCard but not an American Express card is given by P(ABC' )= P(AB )-P(AB C ) = 0.3 - 0.08 = 0.22 Step3: c). consider, P(B/A) = P(BA) P(A) = 0.6 = 0.50 consider, P(A/B) = P(AB) P(B) = 0.3 0.4 = 0.75 d). If we learn that the selected student has an American Express card, the probability that she or he also has both a Visa card and a MasterCard is given by P(ABC) P(A B C/C) = P(C) 0.08 = 0.2 = 0.40 e). Given that the selected student has an American Express card, the probability that she or he has at least one of the other two types of cards is given by P(AB) = P(A) + P(B) - P(A B) = 0.6 + 0.4 - 0.3 = 0.7

Step 2 of 3

Chapter 2, Problem 47E is Solved
Step 3 of 3

Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

This full solution covers the following key subjects: . This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The answer to “47E” is broken down into a number of easy to follow steps, and 1 words. The full step-by-step solution to problem: 47E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Since the solution to 47E from 2 chapter was answered, more than 447 students have viewed the full step-by-step answer.

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Ch 2 - 47E