Chapter 11 - 1

Probability

The measure of the likelihood that an event will occur, expressed as a proportion.

Random Behavior

Outcomes are uncertain for individual trials, but show a regular pattern over a large number of repetitions.

Sample Space

The set of all possible outcomes of a random phenomenon.

Event

A collection of sample points, or a subset of the sample space.

Independent Trials

Trials are independent if the outcome of one does not influence the outcome of another.

Discrete Random Variable

A variable that can take on a countable number of values.

Continuous Random Variable

A variable that can take on any value within a given interval.

Probability Model

A mathematical description of a random phenomenon that consists of a sample space and a way of assigning probabilities to events.

The Fundamental Counting Principle

If one task can be performed in m ways and a second task can be performed in n ways, then both tasks can be done in m × n ways.

Complement Rule

In probability, the rule stating that the probability of an event not occurring is equal to 1 minus the probability of the event occurring.

Probability Distribution

A function that assigns probabilities to each possible value of a random variable.

Normal Distribution

A continuous probability distribution characterized by a symmetrical bell shape, defined by its mean and standard deviation.

Empirical Probability

Probability based on observed data rather than a theoretical model.

Finite Probability Model

A model describing a random phenomenon with a finite number of outcomes.

Relative Frequency

The number of times an outcome occurs compared to the total number of trials.

Tree Diagram

A graphical representation that helps determine the size and members of a sample space.

Legitimate Probability Model

A model that adheres to the rules of probability and has probabilities that sum to 1.

Area Under the Curve

In probability, the area under a density curve represents the probability of outcomes within a given range.

Benford's Law

A probability model for the distribution of first digits in many real-life sources of numerical data.