Question

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then `P(barA) + P(barB)` is ______.

Options

• 0.4

• 0.8

• 1.2

• 1.6

Answer 1

The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then `P(barA) + P(barB)` is 1.2.

Explanation:

Given that: P(A ∪ B) = 0.6

P(A ∩ B) = 0.2

∴ P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

⇒ 0.6 = P(A) + P(B) – 0.2

⇒ P(A) + P(B) = 0.6 + 0.2 = 0.8

And `1 - P(barA) + 1 - P(barB)` = 0.8

⇒ `P(barA) + P(barB)` = 2 – 0.8 = 1.2