Final answer:
The probability of events A and B both occurring is found by multiplying P(B|A), the conditional probability of B given A, with P(A), the probability of A. The calculation yields a result of P(A AND B) = 88/275.
Step-by-step explanation:
To calculate the probability of both events A and B occurring, denoted as P(A AND B), you need to use the formula P(A and B) = P(B|A) × P(A). Here, P(B|A) is the probability of event B occurring given that event A has already occurred, and P(A) is the probability of event A occurring on its own.
Based on the provided information, P(A) = 4/11 and P(B|A) = 22/25. We simply multiply these two probabilities together to find the joint probability of A and B occurring.
P(A AND B) = P(B|A) × P(A) = (22/25) × (4/11) = 88/275