If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.4 and P(A ∪ B) = 0.5, find P(A ∩ B).

Question

Philoid · Accepted Answer

Given A and B are two events

And, P(A) = 0.3 P(B) = 0.5 P(A ∪ B) = 0.5

We need to find P(A ∩ 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(A ∩ B) = P(A) + P(B) – P(A ∪ B)

⇒ P(A ∩ B) = 0.3 + 0.4 – 0.5 = 0.7 – 0.5 = 0.2

∴ P(A ∩ B) = 0.2