Chapter_4.1 Vocabulary

CHAPTER 4:

© Rita Marie O’Brien Chapter 4.1 Page 1 Probability and Counting Rules CHAPTER 4

Slide 2:

© Rita Marie O’Brien Chapter 4.1 Page 2 Introduction Probability is the chance of an event occurring. In addition to being used in games of chance, probability is used in the fields of insurance, investments, and weather forecasting, and in various other areas.

Basic Concepts:

© Rita Marie O’Brien Chapter 4.1 Page 3 Basic Concepts A probability experiment is a chance process that leads to well-defined results called outcomes.

Basic Concepts:

© Rita Marie O’Brien Chapter 4.1 Page 4 Basic Concepts An outcome is the result of a single trial of a probability experiment.

Basic Concepts:

© Rita Marie O’Brien Chapter 4.1 Page 5 Basic Concepts A sample space is the set of all possible outcomes of a probability experiment.

Basic Concepts:

© Rita Marie O’Brien Chapter 4.1 Page 6 Basic Concepts Example: the sample space for rolling two dice

Basic Concepts:

© Rita Marie O’Brien Chapter 4.1 Page 7 Basic Concepts An event consists of the outcomes of a probability experiment.

Basic Concepts:

© Rita Marie O’Brien Chapter 4.1 Page 8 Basic Concepts A simple event is an event with one outcome. A compound event is an event with two or more outcomes.

Basic Concepts (cont’d.):

© Rita Marie O’Brien Chapter 4.1 Page 9 Basic Concepts (cont’d.) Equally likely events are events that have the same probability of occurring. Predictions are based on probability. Hypotheses are tested by using probability.

3 Types of Probability:

© Rita Marie O’Brien Chapter 4.1 Page 10 3 Types of Probability Classical Empirical Subjective

3 Types of Probability:

© Rita Marie O’Brien Chapter 4.1 Page 11 3 Types of Probability Classical probability uses sample spaces to determine the numerical probability that an event will happen. Classical probability assumes that all outcomes in the sample space are equally likely to occur.

Probability Rules:

© Rita Marie O’Brien Chapter 4.1 Page 12 1. The probability of an event E is a number between and including 0 and 1. This is denoted by: Rule: 0 ≤ P(E) ≤ 1 1. States that probabilities cannot be negative or greater than one. Probability Rules

Probability Rules (cont’d.):

© Rita Marie O’Brien Chapter 4.1 Page 13 Probability Rules (cont’d.) 2. If P( E) cannot occur then P(E) = 0 3. If P( E) is certain, then the P( E) = 1. 4. The sum of the probabilities of the outcomes in the sample space is 1. Therefore: 0 ≤ P(E) ≤ 1 the probability of an event will be between 0 and 1.

Complementary Events:

© Rita Marie O’Brien Chapter 4.1 Page 14 or Complementary Events The complement of an event E is the set of outcomes in the sample space that are not included in the outcomes of event E . The complement of E is denoted by Ē (read as E bar). P(E) + P(Ē ) =1

Empirical Probability:

© Rita Marie O’Brien Chapter 4.1 Page 15 Empirical Probability Empirical probability relies on actual experience to determine the likelihood of outcomes. Given a frequency distribution, the probability of an event being in a given class is:

Subjective Probability:

© Rita Marie O’Brien Chapter 4.1 Page 16 Subjective Probability Subjective Probability uses a probability value based on an educated guess or estimate, employing opinions and inexact information. In subjective probability, a person or group makes an educated guess at the chance that an event will occur. This guess is based on the person’s experience and evaluation of a solution.