Question

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

1. 0.24
2. 0.3
3. 0.48
4. 0.96

Answer 1

Correct Answer - Option 4 : 0.96

Concept:

For two events A and B:

• P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
• The conditional probability of A given B is defined as: P(A|B) = \(\rm \dfrac{P(A\cap B)}{P(B)}\), when P(B) > 0.

 

Calculation:

Using the relation P(B|A) = \(\rm \dfrac{P(A\cap B)}{0.4}\), 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.