Final answer:
To calculate P(A ∩ B), we can use the formula P(A ∩ B) = P(A) × P(B|A), where P(B|A) represents the probability of event B occurring given that event A has occurred. Given the values provided, the probability of both events A and B occurring is 0.378.
Step-by-step explanation:
In this question, we are given that P(A) = 0.42, P(B) = 0.17, and P(A ∩ B) = 0.37. We are asked to calculate the probability of both events A and B occurring, which is denoted as P(A ∩ B).
To calculate P(A ∩ B), we can use the formula P(A ∩ B) = P(A) × P(B|A), where P(B|A) represents the probability of event B occurring given that event A has occurred.
Given that P(A ∩ B) = 0.37 and P(B|A) = 0.90, we can substitute these values into the formula to find:
P(A ∩ B) = P(A) × P(B|A) = 0.42 × 0.90 = 0.378
Therefore, the probability of both events A and B occurring is 0.378.