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

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)