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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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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.

Ever taken a chance on something? Before you took that chance, did you want to know what your chances were on actually winning? Then you were dealing with probability, the likelihood that a specific event will occur.

Have you ever flipped a coin? Or maybe you've rolled a pair of dice while playing a board game? Maybe even you've played a game like bingo? In any event, you're relying on events that are, hopefully, determined solely by chance. There is no amount of study or exercise that is going to make you more able to handle such events, as they are entirely random. However, that is not to say that understanding more about them won't help you figure out when something is likely to happen. This measure of how likely something is to occur is called **probability** and allows us to better understand what is happening, even if we can't control the outcome.

Let's say that you had a single die to roll. The die in question is perfectly fair, so it's not likely to help anyone cheat. It is just as likely to land on 3 as it is likely to land on 6. Rolling the die is called an experiment. An **experiment** is the term people who study probability give to anything that involves random chance. Rolling a die is just as much of an experiment as picking the numbers to be drawn in a lottery jackpot.

Go ahead, roll that die. Every time you do, you get an **outcome**. An outcome is the term we give to the result of each attempt at a random exercise. Most often, these are used to describe possibilities. Roll it again. Chances are you come up with something different. In fact, rolling a die can have exactly six outcomes - either you roll a 1, 2, 3, 4, 5, or a 6. Likewise, playing the lottery can have a number of different outcomes - one of the 23 million combinations or so will win the jackpot, a few will win smaller prizes, but 22 million or so combinations will get nothing.

Roll that die a few times. Again, chances are you will land on multiple numbers. The term we give to the outcomes once they have happened are **events**. Likely events when rolling a standard die are to roll a 1, 2, 3, 4, 5, or a 6. An unlikely event is to roll a 12. Again, when someone buys a lottery ticket, they are hoping that across a number of drawings that the possible outcomes match up with the event in question.

All of this probability depends on one thing above all else - every outcome must be equally likely. An **equally likely event** is any event that is equally likely to be any one of the potential outcomes. That's why at the beginning, I told you to make sure that you were playing with a fair die. Only a fair die has the ability to ensure that an event is equally likely. Likewise, lottery companies go to great lengths to make sure that a drawing is equally likely to return one set of numbers as any other. Of course, we could tweak that so that some things are more likely than others, but for this introduction, we'll stick with all things being equal.

So how can we mathematically express the idea of probability? Luckily for us, the formula is pretty simple. All you do is divide the number of ways that an event can happen by the number of potential outcomes. Take that die, for example. There is only one way to roll a six on that die. However, you can roll six different numbers, meaning that you can have six different outcomes. Since there is only one way you can get a 6, you put a one on top, but since there are six different outcomes, you put a six on the bottom. In the end, you get 1/6.

To make things easy, let's say that a lottery has 23 million different possible combinations. However, only one combination of numbers will win the jackpot. Therefore, the probability of winning the jackpot of this lottery is 1 over 23 million. To put that into perspective, you have a likelihood of about 1 in 3,000 of being struck by lightning over your entire lifetime.

In this lesson, we took a look at **probability**, the measure of how likely something is to occur. We learned that an **experiment** is the name given to anything that involves random chance. All the potential results of an experiment are called **outcomes**, while actual results are called **events**. An **equally likely event** is any event that is equally likely to be any one of the potential outcomes. We can measure probability by dividing the number of ways for an event to be true by the number of potential outcomes.

- probability: the measure of how likely something is to occur
- experiment: the name given to anything that involves random chance
- outcomes: all the potential results of an experiment
- events: actual results
- equally likely event: any event that is equally likely to have any one of the potential outcomes

When finished, weigh your capacity to complete these goals:

- Define probability
- Indicate ways in which experiments and outcomes are related to probability
- Explain the way in which an equally likely event is considered to be fair
- Use the probability formula

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Introduction to Probability: Formula & Examples 4:33
- Experimental Probability: Definition & Predictions 3:49
- Probability of Compound Events: Definition & Examples 5:40
- Mutually Exclusive Events & Non-Mutually Exclusive Events 4:58
- Set Theory, Venn Diagrams & Exclusive Events 4:34
- Fundamental Counting Principle: Definition & Examples 5:02
- How to Calculate a Permutation 6:58
- Math Combinations: Formula and Example Problems 7:14
- Go to 6th-8th Grade Math: Probability

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