Question

If P (not B) = 0.65, P (A ∪ B) = 0.85, and A and B are independent events, then find p (A).

Answer 1

We know that,

P (A ∪ B)=P(A) + P(B) – P(A ∩ B)

P(not B) =1 – P(B) =1 – 0.65 = 0.35

Given that A and B are independent events,

Therefore,

P (A ∪ B) = P(A) + P(B) – P(A ∩ B)

= P(A) + P(B) – [P(A)*P(B)]

P (A ∪ B) = P(A)[1 – P(B)] + P(B)

0.85 = P(A)*0.65 + 0.35

P(A)*0.65 = 0.50

P(A) = \(\cfrac{0.5}{0.65} = 0.77\)