Introduction to Probability: Formula & Examples

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  • 0:01 Probability
  • 0:36 Experiments and Outcomes
  • 1:40 Events
  • 2:55 Probability Formula
  • 3:53 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.

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.

Experiments and Outcomes

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.

Events and Equal Likelihood

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.

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