# mutually exclusive events or not

i've been asked to state whether the events A and B are mutually exclusive or not I know that if AnB=0 they are mutually exclusive but I don't understand the test on how to calculate mutually exclusive.

• P(A) = 4/8
• P(B) = 4/8
• P(AnB) = 2/8
• P(AuB) = 6/8

I found that my P(A) + P(B)- P(AnB) was equal to the P(AuB) (4/8) + (4/8) - (2/8) = 6/8 P(AuB) but does this mean they are not mutually exclusive since this test is only applicable if the events are not mutually exclusive? otherwise can you please give me another way to test for mutually excluse

• You're missing a lot of $P$'s throughout your post (for instance $P(A\cap B)=0$ and not $A\cap B=0$). Please edit accordingly. If $P(A\cap B)=2/8$ then $A$ and $B$ can't be mutually exclusive, can they? Mar 12, 2014 at 9:55
• woops! sorry, edited now Mar 12, 2014 at 11:20

If $A\cap B=\emptyset$ (the definition of mutually exclusive) the what must the probability of $A\cap B$ be?
It has been given in the condition that $P(A \cap B) \neq 0$, so this is not a mutually exclusive event.