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)?

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)...