Final answer:
The probability of both independent events A and B occurring, denoted as P(A ∩ B), is calculated by multiplying their individual probabilities, in this case resulting in 0.12.
Step-by-step explanation:
If events A and B are independent, the probability of both events A and B occurring is found by multiplying the probabilities of each event. The formula for this is P(A ∩ B) = P(A) × P(B). Therefore, given that P(A) = 0.3 and P(B) = 0.4 and A and B are independent events, we use the formula to calculate P(A ∩ B).
P(A ∩ B) = P(A) × P(B) = 0.3 × 0.4 = 0.12
Therefore, the probability that both events A and B occur is 0.12.