# Confusion with 'events' and mutually excusive

Suppose two events $A$ and $B$ are mutually exclusive then we say that $P$ ($A \cap B)=0$. In my knowledge event is the outcomes delivered when we preform a task. So in the above line, when two events are mutually exclusive, does that mean any outcome obtained in any one event is different from outcomes obtained in other event? Is that what we use to identify any two events (mutually exclusive, exhaustive etc ).

• Not sure I understand your question. In the set up, one imagines that there is a trial and that, after the trial, we will be able to say whether a given event happened or not. To say the two events are mutually exclusive means that if you tell me that $A$ happened, then I know that $B$ did not and conversely (granted, for continuous distributions we may replace "did not happen" with "happened with probability $0$"). Is this what you are asking? – lulu Nov 10 '17 at 12:27
• Yes, when you do a task (experiment) there are a set of possible outcomes S. Viewed this way, events are subsets of S. Mutually exclusive events (subsets) have no outcomes in common i.e an empty intersection in terms of subsets. Put in real terms, when one event happens the other cannot happen if they are mutually exclusive. – Paul Nov 10 '17 at 12:27
• Just to be clear, given that the events are mutually exclusive, $A\cap B=\emptyset$ (the intersection is the empty set); but the probability is always a number, in this case $P(A\cap B) = 0$ (zero). It's not clear what you meant by "phie". – David K Nov 10 '17 at 12:32
• an event is a subset of the sample space. See here. – Masacroso Nov 10 '17 at 12:41