Let A and B be two independent evens such that PA 0 and PB

Let A and B be two independent evens such that P(A) > 0 and P(B) > 0. Which of the following must be true?

(a) P(AB)=P(A)·P(B)
(b) The two events are not disjoint.

(c) The two events are disjoint.

(d) P(Ac) = P(Bc)

(e) P(A|B) = P(B)

Solution

It must be true that they are NOT DISJOINT. [OPTION B]

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Why?

If they are disjoint, the P(A n B) = 0.

However, P(A n B) = P(A) P(B) > 0, as they are both positive.

Thus, they are NOT DISJOINT.