Final answer:
To find P(A ∩ B) when A and B are independent, multiply P(A) by P(B), resulting in 0.28. For mutually exclusive events A and B, P(A ∪ B) is the sum of P(A) and P(B), but it cannot be calculated without the value of P(B).
Step-by-step explanation:
Finding P(A ∩ B) for Independent Events
When events A and B are independent, the probability of both events occurring simultaneously, represented by P(A ∩ B), is the product of their individual probabilities. Given that P(A)=0.4 and P(B)=0.7, calculating P(A ∩ B) for independent events is as follows:
P(A ∩ B) = P(A) × P(B) = 0.4 × 0.7 = 0.28.
Finding P(A ∪ B) for Mutually Exclusive Events
If events A and B are mutually exclusive, they cannot occur at the same time, which means P(A ∩ B) = 0. The probability of either A or B occurring, P(A ∪ B), is the sum of their individual probabilities. However, since P(B) is not provided in the question, we cannot calculate P(A ∪ B). Thus, we would need P(B) to compute:
P(A ∪ B) = P(A) + P(B).