# Praxis Core Prep: How to Calculate Probability

For the Praxis Core, you will focus on the probability of an event, also known as *P* (event), which deals with how likely something is to occur. You can record the probability of an event as a fraction, decimal, or percent.

A chance action, such as tossing a number cube, is also called an *experiment.* Each observation of the experiment is called a *trial,* and what happens at the end of the trial is the *outcome.* One or more outcomes are called *events.*

When you throw a single die, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. The probability of any one of them occurring is 1/6.

## Determining the likelihood of an event

When you throw a single die, there are six sides and six possible outcomes The table below indicates that the even outcomes are half and the not even outcomes are half; therefore, the likelihood of rolling an even number is as likely to happen or not — you have a 3/6 (read, three in six) or 50-50 chance.

Even | Not Even |
---|---|

2, 4, 6 | 1, 3, 5 |

What is the likelihood that you’ll roll a 6 on the single die? When a single die is rolled, either a 6 will be rolled or it won’t be rolled. There is only one 6 on the single die, so the likelihood that it will be rolled is 1 out of 6.

## Using complements

Are you ready for a complement? The *complement* of an event is the set of all outcomes that are not the event. Analyze the situation that is occurring and find your total possible outcomes.

For example, you have 16 total marbles in a bag, and the marbles are different colors. Write each color as a fraction, decimal, or percent of the total number.

Blue | Red | Green | Black | Total |
---|---|---|---|---|

8/16 | 5/16 | 2/16 | 1/16 | 16/16 or 1 |

The bag contains eight blue marbles, five red marbles, two green marbles, and one black marble. The probability of randomly picking a blue marble is 8/16. What is the probability of not drawing a blue marble? The probability of not picking a blue marble would be 8/16 or the sum of the remaining marbles in the bag. The (P) of not picking blue is the complement.