Explainer: Theoretical Probability

In this explainer, we will learn how to interpret a data set by finding and evaluating the theoretical probabilities.

In probability, when an event is the result of an experiment with a single stage, we say that this is a simple event. So, for example, tossing a coin once is a single stage experiment. The coin landing with the heads facing up is a simple event.

To calculate the probability of a simple event, we need to know the number of ways we can get a favorable outcome (i.e., the number of ways the thing we want to happen can happen) and the total number of all possible outcomes (i.e., the number of things that could possibly happen).

The probability of a simple event 𝐸 occurring is then 𝑃(𝐸)=numberofwaysafavorableoutcomecanoccurtotalpossibleoutcomes.

In our coin tossing example, if our simple event is “getting a heads” in a single throw, then the probability of getting a heads is 𝑃(heads)=12=0.5.

There is one way to get a heads and only two possible outcomes altogether: heads or tails.

Let us look at some examples.

Example 1: Simple Probability: Random Selection of a Game

When Hannah gets home from school every day, she likes to play computer games for a while before starting her homework. She currently has 8 games to choose from and has no particular favorite.