"Either/Or" Probability for Non-Overlapping Events

Video Transcription

In this tutorial, we're going to talk about "or" probability for non-overlapping events. "Or" means that either one or both of these two events happen. And non-overlapping means they can't both happen at the same time.

So that sort of eliminates one of the choices here. We said one or both of these two events happening. But we're saying they can't both happen. So what we mean, is exactly one of them happens.

Let's take a look at an example. Suppose you had two mutually exclusive, or not overlapping events, like selecting a six from a deck, and selecting a face card from a deck of cards. These can't both happen at the same time. If you are selecting a six, then you necessarily not selecting a face card and vice versa.

Now what's the probability of selecting a six or a face card? Well we can just count it out? 1, 2, 3, 4, 5, 6, 7, 8, all the way up to 16. There are 16 sixes or face cards. Four sixes and 12 face cards, out of 52.

Now notice what we did here, four plus 12. We could call this four out of 52, plus 12 out of 52. But think about it. Four out of 52 was the probability of a six. 12 out of 52 was the probability of a face card.

So it would appear, that for non-overlapping events, we can calculate the "or" probability as the probability of A or B occurring, and they can't both happen, would be the individual probabilities added together.

It doesn't work if you have overlapping events. Let's take a look. Probability of a six or diamond. So if we counted out all the things that were either sixes or diamonds, we would end up with 16 out of 52 cards. That's not the same as adding the probability of a six to the probability of a diamond. This would give you 17 out of 52.

So this formula only works for non-overlapping events. And so to recap, if two events A and B, are mutually exclusive, meaning they can't happen at the same time, then the probability that either A or B happens is equal to the probability of A plus the probability of B.

So we talked about the special addition rule for mutually exclusive, or non-overlapping events. This is a special addition rule. Because there will be a different addition rule for if the events are overlapping.

Good luck, and we'll see you next time.