we say two events A and B are mutually exclusive events if it is impossible for both to happen at the same time so what does this mean this means that the two events don't have any outcomes in common specifically mathematically this means that the probability of A and B probability that one of their shared outcomes happens is zero because they don't have any shared outcomes it's impossible for both to happen graphically if we write draw this as a Venn diagram A's right here and B could be right here okay notice they don't overlap at all there's nothing in common there okay so in this case A and B would be mutually exclusive events they have nothing in common it's impossible for both to happen at the same time the probability of both happening at the same time is zero so what's an example let's look at a couple let e be rolling a dice on an even number and D let's let D be rolling a dice on an odd number notice that these two are mutually exclusive events why because they cannot happen at the same time if I roll an even number then I know I have not rolled an odd number and likewise if I roll an odd number then I can't possibly have rolled an even number they cannot happen simultaneously if we write out the outcomes this is even more obvious so if this is standard six-sided die e R would be rolling an even number so you'd roll a 2 a 4 or 6. any of these outcomes would mean that event e has happened whereas event D is when we roll an odd number so that's if we roll a 1 a 3 or a five they don't have any outcomes in common the outcomes in E are not in D and vice versa okay so when this happens these are called mutually exclusive events and a nice thing happens with that addition formula that we learned earlier if the events are mutually exclusive so remember our general addition formula okay that is if I have two events A and B the probability of A or B happening is equal to the probability of a plus the probability of B minus the probability of A and B this formula always is true but in the special case when we know two events are mutually exclusive we can simplify this formula if a and b are mutually exclusive then what do we do we have the same formula okay but then what happens if two events are mutually exclusive then they cannot happen at the same time mathematically that means probability of A and B has to be zero this goes away right so if that is zero then this formula gets a lot easier uh because this term just goes away and so in the special case where am B are mutually exclusive we just have to worry about adding probability of a and probability of B it is that simple now again I need to emphasize that this doesn't always work you do need this condition the events have to be mutually exclusive if they are not mutually exclusive or you are not sure if they are mutually exclusive you need to use this more complicated Edition formula this is a special case only before you use it you must make sure the conditions are met that A and B are mutually exclusive