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

Question

Philoid · Accepted Answer

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