How do you know 2 events are mutually excusive?

mutually exclusive events are never independent

so one way of showing that events are not mutually exclusive is to show they are independent !

but the best way of determining mutual exclusivity is to show that p(A&B) is zero

I think it's B & C. No athlete on the list competes in both the 200m and 110m hurdles, so they are mutually exclusive.

does it equal to zero because both events are mutually exclusive and so can't happen at the same time? Also, is the difference between independent events & mutually exclusive events that independent events can happen at the same time BUT aren't affected by each other and mutually exclusive events just can't happen together?

Thanks

yes... it is like the probability of a coin landing on heads and tails...these events are mutually exclusive ( also exhaustive )

or the probability of a card being hearts and diamonds... these events are mutually exclusive ( but not exhaustive )

Two events are mutually exclusive if the following is true:

If A occurs, then P(B) is unaffected. That is to say P(B|A) = P(B).

That's the definition of independence!

A and B are mutually exclusive if they can't both happen together.

Examples:
I choose a number. A = the event that the number is even. B = the event that the number is odd.

I choose a playing card from a pack. A = the event that it is red. B = the event that it is black.