1. ## Confused About Mutual Exclusivity with More Than Two Events

Hello,

Sorry if this is the wrong section of the forums, but I figured that questions about mutually exclusive events are relevant to probability.

My current understanding:
Two events are mutually exclusive if both events cannot occur at the same time. In other words, two events are mutually exclusive if the probability of both events occurring at the same time is 0.

I guess I'll use an example with fair six-sided dice to try and explain where my confusion lies.

Two Events: The event Roll 1 and the event Roll 3 or 4 are mutually exclusive (none of the six outcomes belong to both events).
Two Events: The event Roll 3 or 4 and the event Roll 4 or 5 are not mutually exclusive (the outcome of 4 belongs to both events).

My question:
Are the three events Roll 1, Roll 3 or 4 and Roll 4 or 5 considered to be mutually exclusive or not mutually exclusive?

On one hand, the three events seem to be not mutually exclusive because two of the three events can occur at the same time. But on the other hand, the three events seem to be mutually exclusive because the probability of all three events occurring at the same time is 0.

Can someone please advise me where the mistake in my thinking lies? Perhaps I'm not using a good definition of mutual exclusivity? Is there a standard definition that I should be using?

Thanks a lot!

2. ## Re: Confused About Mutual Exclusivity with More Than Two Events

Mutually exclusive means the probability of any and all subsets of the events happening simultaneously is zero.

In your example the 3 events are not mutually exclusive as a roll of 4 is a member of the second and third events.

The fact that event 1 is mutually exclusive with both events 2 and 3 doesn't change this.

3. ## Re: Confused About Mutual Exclusivity with More Than Two Events

Originally Posted by romsek
Mutually exclusive means the probability of any and all subsets of the events happening simultaneously is zero.

In your example the 3 events are not mutually exclusive as a roll of 4 is a member of the second and third events.

The fact that event 1 is mutually exclusive with both events 2 and 3 doesn't change this.
Thank you for helping me understand; it's much appreciated!

As a side question, would the events then be considered mutually inclusive?