# Mutually Exclusive Events & Non-Mutually Exclusive Events

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• 0:01 Types of Events
• 0:48 Mutually Exclusive Events
• 1:36 Probability & Mutually…
• 2:46 Non-Mutually Exclusive Events
• 3:24 Probability &…
• 4:21 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

In this lesson, we look at the ideas of mutually exclusive and non-mutually exclusive events. As we will learn, just because two events are non-mutually exclusive events are possible, that doesn't make them likely.

## Types of Events

When figuring out the probability of two or more events happening, we don't just have to look at the chances as determined by a coin toss, die throw, or the whims of the lottery ball machine. Instead, we have to figure out if the multiple events can even happen if one of the events occurs.

We're talking about a mutually exclusive event, which is an event that cannot happen if another event occurs. Meanwhile, a non-mutually exclusive event is an event that can happen no matter what happens to another event. In this lesson, we will look at some examples of both mutually exclusive and non-mutually exclusive events, as well as how each affects probability.

## Mutually Exclusive Events

As already stated, mutually exclusive events are those events that cannot happen if another related event happens. Likewise, if the related event doesn't happen, then a mutually exclusive event can happen. This doesn't necessarily mean that it has to happen.

Take, for example, the roll of a dice. If you roll a six, any other outcome is mutually exclusive. Simply put, it can't happen. However, just because you don't roll a four does not mean that you automatically roll a six.

Let's look at an even bigger example. Say that you were looking at the probability of the lottery drawing two fives. Since there is only one of each ball in the lottery machine, that's impossible. Once the five is drawn, there is no other five in the machine to be drawn.

## Probability and Mutually Exclusive Events

Let's use some probability to see how this looks. Let's say that you were to draw two numbers out of a lottery machine. There are 36 numbers in the machine, so you have a 1 in 36 chance of being able to draw any number out of the machine. However, once that number is drawn, it cannot be drawn again.

Let's say you wanted to draw two fives out, just like we said earlier. You have a 1 in 36 chance, right? So, let's say a few draws in that you manage to fish out that five ball. Now, you want another draw. At this point, you have a 1 in 35 chance of finding any one ball. However, there is an exception. Since the five is already out, it can't be selected and has a zero percent chance.

Let's try another example, this time using sports. The New York Yankees and the Boston Red Sox are two of the fiercest rivals in sports, with a rivalry going back more than 100 years. Still, we can't have a World Series with the Yankees against the Red Sox, because they are both in the same league. As each league sends only one team to the World Series, it is mutually exclusive on the other teams if any one is chosen.

## Non-Mutually Exclusive Events

That wouldn't be a problem with non-mutually exclusive events. Remember, it doesn't matter what happens, since the outcome is unrelated to what happened earlier.

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