CFA Level 1: Calculating Joint Probability - Exam Question Solution

Joint Probability Calculation: P(ABCD)

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Question

Suppose that events A, B, C, and D are independent, and have probabilities of 0.25, 0.50, 0.40, and 0.30, respectively. What is P(ABCD)?

Answers

Explanations

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A. B. C. D.

C

If events are independent, then the joint probability of them occurring together is just the product of the individual probabilities. So P(ABCD) = 0.25 * 0.50 * 0.40 *

0.30 = 1.5%.

To calculate the probability of the joint event ABCD, we need to multiply the probabilities of each individual event since they are independent.

The probability of event A is 0.25, which means that in any given trial, the chance of event A occurring is 0.25.

Similarly, the probability of event B is 0.50, the probability of event C is 0.40, and the probability of event D is 0.30.

To find the probability of the joint event ABCD, we multiply the probabilities of each individual event:

P(ABCD) = P(A) * P(B) * P(C) * P(D)

P(ABCD) = 0.25 * 0.50 * 0.40 * 0.30

P(ABCD) = 0.015

So the probability of the joint event ABCD is 0.015 or 1.5%.

Therefore, the correct answer is C. 1.5%.

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