The probability that at least one of the events A and B… — JEE Main 1987 Mathematics PYQ

1987

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 equal to

Show answer and solution

Correct option: C

Solution

P(A∪B) = P(A) + P(B) - P(A∩B), so 0.6 = P(A) + P(B) - 0.2, giving P(A) + P(B) = 0.8. Then P(Ā) + P(B̄) = (1 - P(A)) + (1 - P(B)) = 2 - 0.8 = 1.2.

[1987]

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JEE Main 1987 Mathematics question on Probability