Probability Terminology: Boolean Algebra, Probability Space & Sample Space

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  • 0:04 What Is Probability?
  • 0:35 Boolean Algebra
  • 1:06 Sample Space
  • 2:05 Probability Space
  • 3:14 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

In this lesson, learn about how to use Boolean algebra to determine the sample space and probability space for an experiment. Learn what these terms mean and how to apply them.

What Is Probability?

If you flipped a set of four coins 100 times, how many times would you expect for all four coins to land on heads? The chance that each individual coin toss will result in four heads is known as the probability that the event will occur. In this case, there is actually a low probability that the coins will all land on heads. There's a much greater probability that some will be heads and some will be tails. Let's see if we can determine exactly why this is the case and how to represent all the possible outcomes of the coin toss.

Boolean Algebra

Before you can understand how to determine the probability that a certain event will occur, you need to know a little bit about a special kind of math called Boolean algebra. Boolean algebra is a branch of math that doesn't use numbers, but instead uses values that can either be true or false.

A coin toss is a great example of a system that can be represented with Boolean algebra, because it only has two possible outcomes: heads or tails. One of these outcomes can be considered to be true, and the other will then be false.

Sample Space

In any experiment, there are always multiple possible outcomes. Every time you flip the coin, there is a 50% chance of it landing on heads (and a 50% chance of it landing on tails, of course).

The sample space of the experiment is defined as all the possible outcomes that can occur. In our coin toss experiment, we flipped four coins. What is the sample space for this experiment? It should include all the possible outcomes of each coin flip, for a total of sixteen possibilities, as you can see listed out on your screen right now:

coin toss sample space

In this sample space, we can see that there are 18 possible outcomes. Of those, one results in four heads and one in zero heads (four tails). Four possible outcomes give you three heads and four more give you one heads. Finally, six different potential outcomes would give you two heads and two tails, making this the most likely result of the coin toss. Exactly how likely is it, though? Let's look at the probability space to find out.

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