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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!