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Mutually Exclusive Events
In the next couple of videos we’re going to be building up the Or rule and the And rule, two major rules in probability. In order to get there, first we need to discuss the idea of Mutually Exclusive. So, what do we mean by this? Two events are mutually exclusive if it is impossible for both of them to happen at the same time.
If one happens, it absolutely precludes the possibility that the other happens. Sometimes in other textbooks you’ll see the word disjoint used these two event are disjoint that’s just a synonym for mutually exclusive. So let’s think about this. If we say, events A and B are mutually exclusive, what that means, it’s possible that A could happen alone, it’s possible that B could happen alone, it’s possible that neither one of them could happen, that’s also fine.
The only thing that is impossible is that they both happen together. Saying that they are mutually exclusive is saying that it is impossible for both of them to happen together. And we could write this symbolically as the probability of A and B is 0. Well, this is a distinction that is most useful for very simple systems: dice, coins, cards.
So for example, with a dice, if I, if I roll one die, I could get a 2 or I could get a 3, but getting a 2 and a 3 at the same time, those who are mutually exclusive, that’s just not gonna happen. If I pick a card out of a deck, it could be a spade, it could be a club. But there’s no way that it’s going to be both a spade and a club at the same time.
Those two are mutually exclusive. So that’s the type of scenario where mutually exclusive shows up. I point out that it gets far trickier when you start looking at sociological categories. When you start looking at human data about political parties and people’s religions and you know.
Cuz mostly if someone’s a member of this religion there’re not going to be a member of that religion. But sometimes you will run into somebody who’s a member of two religions at once, or a member of two political parties at once, or bi-racial, or any one of a number of combinations.
So that the idea of disjoint gets much harder to apply when we’re talking about human situations. Again, it is most applicable in these very simple situations.
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