Source: Images created by the author; Playing Cards; Public Domain: http://www.jfitz.com/cards/
In this tutorial, you're going to learn about overlapping events. Overlapping means that two events can occur both at the same time. So let's look at an example.
In picking a card from a deck, you might pick a six. You also might pick a diamond. You also might pick both a six and a diamond.
The events six and diamond are overlapping because the events six have four outcomes. The event diamond has 13 outcomes. And there's at least one outcome that's the same in both of them. So the event six and diamond can happen at the same time if you pick the six of diamonds.
Conversely, non-overlapping events are events that can't happen at the same time. The events six and face card are not overlapping. If you pick a six, you're necessarily not picking a face card. And vice versa, if you're picking a face card, you're necessarily not picking a six.
There are a couple different names for non-overlapping. Disjoint and mutually exclusive are two other terms that are used for non-overlapping events. Those are both very common terms.
So we can show either overlap or non-overlap in a Venn diagram. Suppose that we have these two events from rolling a die. Rolling an even is event A. And rolling a five is event B. If you're rolling an even, you're certainly not rolling a five. And vice versa-- if you're rolling a five, you're certainly not rolling an even number. So in a Venn diagram, we show those as two circles that don't have the overlap portion between them.
And non-overlapping events can't be independent. The thing is, with independent events, knowing what happened with event A doesn't change the probability that B will occur. Whereas with disjoint events, or mutually exclusive events, knowing that event A occurred changes the probability of B. In fact, we know what it changes it to. It changes it to zero because B can't happen if A has occurred.
And so to recap, oftentimes two randomly selected events will overlap, which means they can happen at the same time. However, non-overlapping events or disjoint events or mutually exclusive events cannot happen at the same time. Meaning if one happens, then the other one doesn't happen.
So we talked about the difference between overlapping versus non-overlapping. Good luck. And we'll see you next time.
Two events that cannot both occur in a single trial of a chance experiment. If one event occurs, the other event must not also occur.
Two events that can occur in a single trial of a chance experiment.