Question

Let A and B are two events such that the probability that exactly one of them occurs is 2/5 and the probability that A or B occurs is 1/2. Find the probability of both of them occurring together.

A. 0.01
B. 0.10
C. 0.20
D. 0.02

Answer 1

The probability of two independent events A and B occurring together is found by multiplying their individual probabilities: P(A AND B) = P(A) × P(B), resulting in 0.06.

Step-by-step explanation:

The question is about calculating the probability of two events occurring together, given that they are independent. To find the probability that both events A and B occur together, denoted as P(A AND B), we can use the multiplication rule for independent events. The rule states that if A and B are independent, then P(A AND B) = P(A) × P(B).

In this case, we have been given P(A) = 0.2 and P(B) = 0.3 for two independent events. Applying the multiplication rule:

P(A AND B) = P(A) × P(B) = 0.2 × 0.3 = 0.06

Let's denote the probability of event A occurring as P(A) = 0.2 and the probability of event B occurring as P(B) = 0.3. Since A and B are independent events, the probability of both of them occurring together (A AND B) can be calculated as P(A) * P(B) = 0.2 * 0.3 = 0.06.

Therefore, the probability of both events A and B occurring together is 0.06, which corresponds to choice D.