Question

Is it possible for A and B to be in- dependent events yet satisfy A = B?

Answer 1

No, Is it not possible for A and B to be in- dependent events yet satisfy A = B?

Actually if two events are mutually exclusive it is only in a special case that they can be independent. The definitions state that two events A, B are mutually exclusive iff: P (A ∩ B) = 0, i.e. A ∩ B = ∅, independent iff: P (A ∩ B) = P (A) P (B). Assume know that A, B are both mutually exclusive and independent.

Answer 2

Two events A and B can be independent and yet satisfy A = B. In this case, the two events are identical, for example 'getting a head on the first flip' and they are always independent of themselves.

Step-by-step explanation:

Yes, it is possible for events A and B to be independent and yet satisfy A = B. In probability theory, two events are considered independent if the probability of both events occurring is the product of the probabilities of each event occurring separately. If A = B, it merely means that the two events are identical. For instance, flipping a coin twice, the event A could be 'getting a head on the first flip' and event B could also be 'getting a head on the first flip'. Here, A = B and every event is independent of itself.

Learn more about Event Independence