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# Suppose that A and B are two events such that P( A) = .8 ISBN: 9780495110811 47

## Solution for problem 86E Chapter 2

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(A B) = 0.1.

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

c). We need to check P(A B) = 0.77.

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

Step2 of 5:

a).

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

Let P(A B) 1

Where,

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

Consider,

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

0.8 + 0.7 - 0.1 1

1.4 > 1

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

Step3 of 5:

b).

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

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

Step 2 of 3

Step 3 of 3

##### 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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