If A and B are independent events, show that A_ and B are

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 73E Chapter 2

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

Textbook Solutions
2901 Step-by-step solutions solved by professors and subject experts
Get 24/7 help from StudySoup virtual teaching assistants

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

4 5 1 315 Reviews

Problem 73E

If ?A ?and ?B ?are independent events, show that ?A?_ and ?B ?are also independent. [?Hint: ?First establish a relationship between P(A ’?B), P(B), and P(A?B).]

Step-by-Step Solution:

Answer: Step 1 of 1 By definition, A and B independent P(A B) = P(A)P(B). But B = (A B) + (A B) So P(B) = P(A B) + P(A B)1 which yields P(A B) = P(B) - P (A B) = P(B) - P(A) P(B) [since A and B are independent] = P(B)(1 - P(A)) 1 = P(B)P(A ) Therefore, A and B are independent.

Step 2 of 1

Chapter 2, Problem 73E is Solved

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 textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Since the solution to 73E from 2 chapter was answered, more than 368 students have viewed the full step-by-step answer. The answer to “If ?A ?and ?B ?are independent events, show that ?A?_ and ?B ?are also independent. [?Hint: ?First establish a relationship between P(A ’?B), P(B), and P(A?B).]” is broken down into a number of easy to follow steps, and 26 words. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111. The full step-by-step solution to problem: 73E from chapter: 2 was answered by , our top Statistics solution expert on 05/06/17, 06:21PM. This full solution covers the following key subjects: independent, hint, Events, establish, also. This expansive textbook survival guide covers 18 chapters, and 1582 solutions.