PROBLEM 7E

Given that P(A ∪ B) = 0.76 and P(A ∪ B' ) = 0.87, find P(A).

Answer :

Step 1 of 1 :

Given,

P(AB) = 0.76 and P() = 0.87

The claim is to find the value of P(A)

Where,

P() = 1 - P(B) + P() = 0.87

0.87 = 1 - P(B) + P()

P(B) + P() = 1 - 0.87

Therefore, P(B) - P() = 0.13

We know that

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

Where, P(A) = P(AB) - ( P(B) - P())

We have , P(AB) = 0.76 and P(B) - P() = 0.13

Substitute the values in above equation

Then we get

P(A) = 0.76 - 0.13

= 0.63

Hence, P(A) = 0.63