Let E and F be non-zero-probability events. If E and F are mutually-exclusive, can they also be independent? Explain the answer, and also prove it algebraically using the definitions of mutually-exclusive and independent events.
First, let me provide some definitions and examples:
Mutually Exclusive Events
Two events are mutually exclusive if they cannot occur at the same time. In another word, that means mutually exclusive is identical to being disjoint.
If two events are disjoint, then the probability of them both occurring at the same time is 0.
That is, P(A and B) = 0 ------(a)
This is a proof regarding independent and mutually exclusive events.