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Suppose that A and B are two events such that P( A) = .8

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 86E Chapter 2

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 86E

Suppose that A and B are two events such that P( A) = .8 and P( B) = .7.

a Is it possible that P( A ∩ B) = .1? Why or why not?

b What is the smallest possible value for P( A ∩ B)?

c Is it possible that P( A ∩ B) = .77? Why or why not?

d What is the largest possible value for P( A ∩ B)?

Step-by-Step Solution:
Step 1 of 3

Solution 86E

Step1 of 5:

Let us consider two events A and B such that P(A) = 0.8 and P(B) = 0.7

Here our goal is:

a). We need to check P(AB) = 0.1.

b). We need to find the smallest possible value for P(AB).

c). We need to check P(AB) = 0.77.

d). We need to find the largest possible value for P(AB).

Step2 of 5:

a).

No,  P(AB) 0.1 because from the additional rule of probability.

Let P(AB) 1

Where,

                                             P(AB) = P(A) + P(B) - P(AB)   [additional rule of probability is]                                    

Consider,

                                                      P(A) + P(B) - P(AB)1

                                                                             

                                                                    0.8 + 0.7 - 0.11

                                                   

                                                                                      1.4 > 1  

Hence,  P(AB) must be less than or equal to one but here P(AB) is greater than one therefore P(AB) 0.1.

Step3 of 5:

b).

We know that P(AB) = P(A) + P(B) - P(AB)

To find the smallest value of P(AB) we need to ut P(AB)...

Step 2 of 3

Chapter 2, Problem 86E is Solved
Step 3 of 3

Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

Since the solution to 86E from 2 chapter was answered, more than 360 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Events, largest, smallest, such, suppose. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. The answer to “Suppose that A and B are two events such that P( A) = .8 and P( B) = .7.a Is it possible that P( A ? B) = .1? Why or why not?b What is the smallest possible value for P( A ? B)?c Is it possible that P( A ? B) = .77? Why or why not?d What is the largest possible value for P( A ? B)?” is broken down into a number of easy to follow steps, and 69 words. The full step-by-step solution to problem: 86E from chapter: 2 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7.

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