A and B are two events such that P(A) = 0.3 and P ( A∪B)

Home » Aptitude » Probability » Question

A and B are two events such that P(A) = 0.3 and P ( A∪B) = 0.8. If A and B are independent, then P (B) is

1. 2/3
2. 3/8
3. 2/7
4. 4/7
5. None of the above

Correct Option: E

Let P(B) = x
Given, P(A∪B) = 0.8 and P(A) = 0.3
⇒ P(A) + P(B) - P(A∩B) = 0.8
⇒ P(A) + P(B) - P(A) P(B) = 0.8 {∵A and B are independent}
⇒ 0.3 + x - 0.3x = 0.8
⇒ 0.7x = 0.5
∴ x = 5/7