# Probability of mutually exclusive events discussed

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

Â© BrainMass Inc. brainmass.com May 24, 2023, 1:28 pm ad1c9bdddfhttps://brainmass.com/math/probability/probability-mutually-exclusive-events-discussed-22885

#### Solution Preview

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)

If ...

#### Solution Summary

This is a proof regarding independent and mutually exclusive events.

$2.49