Section 15.1: Outcomes and Events

Property

An experiment is an activity whose results can be observed and recorded. Each of the possible results of an experiment is an outcome. The set of all possible outcomes for an experiment is a sample space. The sample space $S$ for rolling a fair die is $S = \{1, 2, 3, 4, 5, 6\}$. An event is a collection of outcomes, a set in the sample space. The set of all even-numbered rolls $\{2, 4, 6\}$ is a subset of all possible rolls of a die $\{1, 2, 3, 4, 5, 6\}$ and is an event.

Examples

• Flipping a coin is an experiment. The sample space is $\{H, T\}$. The event of getting heads has one outcome.
• Picking a random letter from "MATH" is an experiment. The sample space is $\{M, A, T, H\}$. The event of picking a vowel has one outcome, $A$.
• Spinning a spinner with sections Red, Blue, and Green is an experiment. The sample space is {Red, Blue, Green}. The event of landing on a primary color includes two outcomes: Red and Blue.

Explanation

Think of probability as a game. An "experiment" is the action, like rolling a die. An "outcome" is one possible result, like rolling a 4. The "sample space" is all possible results, and an "event" is any group of outcomes.

Property

To count favorable outcomes for an event, identify all outcomes from the sample space that satisfy the event's condition. The number of favorable outcomes is denoted as $n(E)$ where $E$ represents the event.

Examples

Property

Two events are complementary if they are mutually exclusive (have no outcomes in common) and together they make up the entire sample space. The complement of event $X$ is referred to as "not $X$" and contains all outcomes in the sample space that are not in event $X$.

Examples