Chapter 4 Vocab

Collectively exhaustive events

A set of events are collectively exhaustive if one of the events MUST occur. Heads and tails are also collectively exhaustive. One of them must occur.

Sample space

The collection of all possible events. The sample space for flipping a coin is heads and tails. The sample space of rolling a die is 1-6. And so forth.

Joint event

An event that has two or more characteristics, like flipping a coin and getting heads twice in a row.

Marginal probability

Consists of a set of joint probabilities.

Subjective probability

Differs from person to person. Usually based on a combination of an individual's past experience, personal opinion, and analysis of a particular situation. Especially useful in making decisions in situations where a priori or empirical probabilities cannot be used.

Event

Each possible outcome of a variable. A simple event is described by a single characteristic. A coin has two possible events. Roll of die has six. Roll of die and get an EVEN NUMBER has three events. And so forth.

Empirical probability

Probabilities are based on observed data, not on prior knowledge of a process. Empirical probabilities are generated by surveys, for example.

General addition rule (sum rule)

Probability of A OR B is equal to the probability of A plus the probability of B MINUS the probability of A AND B.

Joint probability

Refers to the probability of an occurrence involving two or more events. For example, getting two heads' in a row in a coin toss.

Intersection of events

The chance of ALL of two or more events occurring.

Union of two events

The chance of ANY of two or more events occurring.

Complement

The complement of event A (represented by A') includes all events that are not part of A. So the complement of getting heads is getting tails. Or the complement of rolling a die and getting 5 is getting anything other than 5, so the 5 has five complement events.

Probability

The numeric value representing the chance, likelihood, or possibility that a particular event will occur. An event that has no chance of occurring (an impossible event) has a probability of 0, and an event that is certain to occur (a certain event) has a probability of 1.

Simple probability

The probability of occurrence of a simple even, P(A). Number of households planning to buy a big-screen tv, for example, divided by the total number of households.

a priori probability

The probability of success is based on prior knowledge of the process involved.

Independent Events

Two events are considered independent if the occurrence of one doesn't affect the probability of the other occurring.

Mutually exclusive events

Two events are mutually exclusive if they cannot occur simultaneously. Heads and tails are mutually exclusive.

Bayes' Theorem

Used to revise previously calculated probabilities based on new information.