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A certain legislative committee consists of 10 senators. A

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 90E 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 90E

A certain legislative committee consists of 10 senators. A subcommittee of 3 senators is to be randomly selected. a. How many different such subcommittees are there? b. If the senators are ranked 1, 2,..., 10 in order of seniority, how many different subcommittees would include the most senior senator? c. What is the probability that the selected subcommittee has at least 1 of the 5 most senior senators? d. What is the probability that the subcommittee includes neither of the two most senior senators?

Step-by-Step Solution:
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Problem 90E Answer: Step1: We have A certain legislative committee consists of 10 senators. A subcommittee of 3 senators is to be randomly selected. Our goal is to find, a. How many different such subcommittees are there b. If the senators are ranked 1, 2,..., 10 in order of seniority, how many different subcommittees would include the most senior senator c. What is the probability that the selected subcommittee has at least 1 of the 5 most senior senators d. What is the probability that the subcommittee includes neither of the two most senior senators Step2: a). We can choose the first senator in 10 ways, the second one in 9 ways, the third one in 8 ways, since the order doesn’t matter we need to divide this number by the number of ways we can arrange 3 people, which is 3 × 2 × 1. So finally the number of ways we can choose 3 senator is : 10×9×8 720 3×2×1 = 6 = 120. b). We only need to choose 2 senators since the the third one must be the most senior.there are 9 possibilities for the one and 8 for the second. This senator can be arranged in 2×1 ways. So the total number is: 9×8 72 2×1 = 2 = 36. c). If A - has one of the 5 most senior then we can calculate P(A) as P(A) = 1 - P(A ) 1 1 Since A is the only has senators from the 5 less senior we can calculate P(A) as : P(A) = 1 - P(A )1 5×4×3 = 1 - 3×2×1 120 = 1 - 10 120 = 1 - 0.0833 = 0.9166.

Step 2 of 3

Chapter 2, Problem 90E is Solved
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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: senators, most, subcommittee, senior, subcommittees. This expansive textbook survival guide covers 18 chapters, and 1582 solutions. The full step-by-step solution to problem: 90E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. The answer to “A certain legislative committee consists of 10 senators. A subcommittee of 3 senators is to be randomly selected. a. How many different such subcommittees are there? b. If the senators are ranked 1, 2,..., 10 in order of seniority, how many different subcommittees would include the most senior senator? c. What is the probability that the selected subcommittee has at least 1 of the 5 most senior senators? d. What is the probability that the subcommittee includes neither of the two most senior senators?” is broken down into a number of easy to follow steps, and 84 words. 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 90E from 2 chapter was answered, more than 1103 students have viewed the full step-by-step answer.

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A certain legislative committee consists of 10 senators. A