Define each of the following.


c. Event

Verified step by step guidance

1. Understand that in probability and statistics, an 'event' is a fundamental concept related to outcomes of an experiment or a random process.
2. An event is defined as a set of one or more outcomes from the sample space of a random experiment.
3. The sample space, denoted as \(S\), is the set of all possible outcomes of the experiment.
4. Formally, if \(S\) is the sample space, then an event \(E\) is any subset of \(S\), i.e., \(E \subseteq S\).
5. Events can be simple (consisting of a single outcome) or compound (consisting of multiple outcomes).

Key Concepts

Event

In probability theory, an event is a specific outcome or a set of outcomes from a random experiment. It is a subset of the sample space, which includes all possible outcomes. Events can be simple (one outcome) or compound (multiple outcomes combined). Understanding events is fundamental to calculating probabilities.

Sample Space

The sample space is the complete set of all possible outcomes of a random experiment. It provides the context within which events are defined. For example, when rolling a die, the sample space is {1, 2, 3, 4, 5, 6}. Knowing the sample space is essential to identify and analyze events.

Probability

Probability measures the likelihood that an event will occur, expressed as a number between 0 and 1. It is calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space. Understanding probability helps quantify uncertainty related to events.