Final answer:
The probability of event B, given that A and B are independent events, can be found using the product rule. With P(A) = 0.42 and P(A AND B) = 0.25, P(B) is approximately 0.5952.
Step-by-step explanation:
The subject of this question is the calculation of the probability of an event B given that events A and B are independent, and the probabilities of event A and both A and B occurring together are known. Since A and B are independent events, the product rule for independent events applies, which states that P(A AND B) is equal to P(A) multiplied by P(B).
To find P(B), we can use the formula:
P(A AND B) = P(A) × P(B)
Given P(A AND B) = 0.25 and P(A) = 0.42, we can rearrange the formula to solve for P(B):
P(B) = P(A AND B) / P(A)
Thus: P(B) = 0.25 / 0.42 ≈ 0.5952