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Overlapping Events

Overlapping Events

Description:

This lesson will explain overlapping and non-overlapping events

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Tutorial

What's Covered


In this tutorial, you're going to learn about overlapping events. Specifically you will focus on:

  1. Overlapping Events


1. 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. There's at least one outcome that's the same in both of them. 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.

Terms to Know

Overlapping Events

Two events that can occur in a single trial of a chance experiment

Non-Overlapping

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.

If you pick a six, you're not picking a face card, and vice versa, if you're picking a face card, you're not picking a six.

Disjoint and mutually exclusive are two other terms that are used for non-overlapping events. Those are both very common terms.

You can show either overlap or non-overlap in a Venn diagram. Suppose you 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 if you're rolling a five, you're certainly not rolling an even number. In a Venn diagram, you show those as two circles that don't have the overlap portion between them.

Non-overlapping events can't be independent. 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.


Summary

Oftentimes two randomly selected events will be overlapping, 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.


Good luck..

Source: This work adapted from Sophia Author Jonathan Osters.

TERMS TO KNOW
  • overlapping events

    Two events that can occur in a single trial of a chance experiment.

  • Non-overlapping/Disjoint/Mutually Exclusive Events

    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.