# Are the two events mutually exclusive?

Two fair die are rolled.Let x be that the first die shows an even number and y be an event that the second die shows an odd number.

Are the two events mutually exclusive?

I'm having difficulty in understand what mutually exclusive means.I searched a lot on the net but its still not clear.All it says is that "if two events cannot occur simultaneously they are mutually exclusive". Any help appreciated.

• Do you understand what "occuring simultaneously" means? – miradulo Apr 7 '16 at 20:03
• Does the first event stop the second from happening? If yes, they are mutually exclusive. – Paul Apr 7 '16 at 20:06
• Here the first doesn't stop the second.Right?@Paul so they are not mutually exclusive? – user220382 Apr 7 '16 at 20:13
• True. They are independent though, which is essentially that whether one event happens has no effect on whether the other does (or not). This means that mutually exclusive events are about as far as possible different from independent events. – Paul Apr 8 '16 at 10:33

Two events are mutually exclusive, if they cannot happen at the same time. The two events $x$ and $y$ are mutually exclusive, when $$x\cap y = \emptyset.$$