Question

What must be true for P (A and B) = P(A) x P(B)?

a. A and B cannot be independent.
b. A and B must be disjoint.
c. A and B must be independent.
d. A and be cannot be disjoint.
e. It is always true.

Answer 1

Answer: Choice C) A and B must be independent

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In general,
P(A and B) = P(A)*P(B|A)
and
P(A and B) = P(B)*P(A|B)

The only time P(A) = P(A|B) and P(B) = P(B|A) are true is when A and B are independent. In other words, one event occurring does not alter the probability of the other event.