Q28 of 43 Page 296

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 (bar a) + P (bar b) is

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)

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