Final answer:
True, the probability of the intersection of two events (A and B) cannot exceed the probability of either event alone, so p(a∩b) is less than or equal to 0.45.
Step-by-step explanation:
The statement 'If p(a)=0.45 then for any event b we have p(a∩b)≤0.45' is true. This is because the probability of the intersection of two events, A and B (represented as p(a∩b)), cannot exceed the probability of either event alone. Since we are given that the probability of event A occurring is 0.45, the maximum probability that both A and B can occur simultaneously is also 0.45. In fact, the probability of A and B occurring together could be less than or equal to 0.45 depending on the relationship between events A and B. If events A and B are independent, then the probability of both A and B occurring would be the product of their individual probabilities. If events A and B are mutually exclusive (cannot occur at the same time), then p(a∩b) would be zero.