If A and B are two events associated with a random experiment such that P(A ∪ B) = 0.8, P(A ∩ B) = 0.3 and = 0.5 , find P(B).

Question

Philoid · Accepted Answer

Given A and B are two events

And, P(A’) = 0.5 P(A ∩ B) = 0.3 P(A ∪ B) = 0.8

∵ P(A’) = 1 – P(A) ⇒ P(A) = 1 – 0.5 = 0.5

We need to find P(B).

By definition of P(A or B) under axiomatic approach(also called addition theorem) we know that:

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

∴ P(B) = P(A ∪ B) + P(A ∩ B) – P(A)

⇒ P(B) = 0.8 + 0.3 – 0.5 = 1.1 – 0.5 = 0.6

∴ P(B) = 0.6