- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occur
CFA Practice Question
Which of the following is (are) true?
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.
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. |