CFA Practice Question

There are 410 practice questions for this study session.

CFA Practice Question

Which of the following is (are) true?

I. If P(A or B) = P(A) + P(B), then A and B are independent.
II. If P(A and B) = P(A) x P(B), then A and B are mutually exclusive.
III. If P(A and B) = P(A) + P(B), then P(A) = P(B) = 0.
A. III only
B. II & III
C. I only
Explanation: If A and B are independent, P(A and B) = P(A) x P(B) and vice versa. If A and B are mutually exclusive, P(A and B) = 0.

Note that P(A or B) = P(A) + P(B) - P(A and B). Hence, if P(A and B) = P(A) + P(B), then P(A or B) = 0. This implies that neither A nor B can occur, giving P(A) = P(B) = 0.

User Contributed Comments 4

User Comment
examcfa mutually exclusive P(AlB) and P(BlA) = 0
mekc this one is confusing me
Celsius2222 If P(AorB)=P(A)+P(B), then A & B have to be mutually exclusive, but not necessarily independent;

If P(AandB)=P(A)xP(B), then A & B have to be independent, but not necessarily mutually exclusive.
CJPerugini It's easier to see if you draw it out. Remember P(A and B) references the overlapping area of the two events.That means the overlapping area can never equate to more than the sum of the two events and will only equate to the sum of the two events if both of their areas are 0.
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