• Identify possible outcomes of a chance experiment

What is Probability?

A chance experiment involves making an observation in a situation where there is uncertainty about which of two or more possible outcomes will result.

This list of all possible outcomes of a chance experiment is called the sample space.

In some situations, all of the possible outcomes of a chance experiment occur with the same probability. For example, when a fair six-sided die is rolled, the numbers 1, 2, 3, 4, 5, and 6 are all equally likely to occur (we say these are “equally likely outcomes”). When dealing with equally likely outcomes, it is sometimes helpful to list (or count) all of the possible outcomes.

For a chance experiment, we are often interested in how likely a particular outcome (or collection of outcomes) is. An outcome or collection of outcomes for a chance experiment is called an event.

probability

The probability of an event is a numeric measure of how likely the event is to happen.

Note the conventional notation [latex]P(\text{event})[/latex] indicates the probability of an event.

When the outcomes are equally likely, we can use the following formula to calculate the theoretical probability of event A:

[latex]\text{Probability of }A = P(A) = \dfrac{\text{number of outcomes in event } A}{\text{number of all possible outcomes}}[/latex]

Notice that a probability can be determined by thinking of it as two counting problems followed by the computation of a related fraction.