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If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive....

If P(A) = 0.4 and P(B) = 0.6, then A and B must be collectively exhaustive. True False

Could you please explain why?

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Answer #1

False

For two events A and B to be collectively exhaustive, P(A U B) must be equal to 1

P(A U B) = P(A) + P(B) - P(A B)

In this case, A and B will be collectively exhaustive if

0.4 + 0.6 - P(A B) = 1

That is P(A B) = 0

But we are not sure if P(A B) = 0 because it is not given that the events are mutually exclusive. Therefore, even if it is possible that A and B is collectively exhaustive, it is not true always. It is true only in the particular case where P(A B) = 0. In all other cases, they are not collectively exhaustive.

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