If P(A) = 0.4, P(B) = 0.8 and P(B|A) = 0.6, then P(A ∪ B) is equal to:

Question

Question

Answer 1

Concept:

For two events A and B:

P(B|A) = \(\rm \dfrac{P(A\cap B)}{P(A)}\), when P(A) > 0

Calculation:

Using the relation P(B|A) = \(\rm \dfrac{P(A\cap B)}{P(A)}\), we get:

0.6 = \(\rm \dfrac{P(A\cap B)}{0.4}\)

⇒ P(A ∩ B) = 0.24

Now using the relation P(A ∪ B) = P(A) + P(B) - P(A ∩ B), we get:

P(A ∪ B) = 0.4 + 0.8 - 0.24 = 0.96.