Final answer:
For mutually exclusive events a and b, the probability of both events occurring together, P(a ∩ b), is 0.
Step-by-step explanation:
Mutually exclusive events refer to situations where the occurrence of one event implies the non-occurrence of the other. In this case, with events a and b being mutually exclusive and having respective probabilities of P(a) = 0.3 and P(b) = 0.5, it is crucial to understand that the probability of both events happening simultaneously, denoted as P(a ∩ b), is inherently zero. This result arises from the fundamental principle that mutually exclusive events cannot coexist. Therefore, the probability of their intersection, the joint occurrence, is null. This mathematical concept underscores the clear separation and independence of these events, as they cannot happen concurrently.