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 (\(\overline A\)) + P (\(\overline B\)) is A. 0.4 B. 0.8 C. 1.2 D. 1.6 Select the correct answer from above options

Answer 1

We have, P( atleast one of the events A and B occurs) = 0.6 i.e. P(A ⋃ B) = 0.6 and P(A and B occur simultaneously) = 0.2 i.e. P(A ⋂ B) = 0.2 By General Addition Rule, P(A) + P (B) – P(A ⋂ B) = P(A ⋃ B) ⇒ P(A) + P(B) – 0.2 = 0.6 ⇒ P(A) + P(B) = 0.6 + 0.2 ⇒ P(A) + P(B) = 0.8 …(i) Now, by Complement Rule P(A) = 1 – P(A’) and P(B) = 1 – P(B’) So, eq. (i) become 1 – P(A’) + 1 – P(B’) = 0.8 ⇒ 2 – [P(A’) + P(B’)] = 0.8 ⇒ 2 – 0.8 = P(A’) + P(B’) ⇒ P(A’) + P(B’) = 1.2 Hence, the correct option is (c)