Let A and B be events with P(A) = 0.3 and P(A ∪ B) = 0.7.

a. For what value of P(B) will A and B he mutually exclusive?

b. For what value of P(B) will A and B be independent?

Step 1 of 3:

Let A and B are events with probability P(A)=0.3 and P(AB) =0.7.

We have to find

For what value of P(B) , the events A and B are mutually exclusive. For what value of P(B) , the events A and B are independent.Step 2of 3:

Mutually exclusive events are events that cannot occur simultaneously,which means they are disjoint.

That is,

P( = 0

P(A= P(A) + P(B)

P( = 0.7

P(A) = 0.3

P(B) = P(- P(A)

= 0.4

That means when P(B) =0.4 the events A and B are mutually exclusive.