Chapter 4 - Probability & Counting Rules

Venn Diagram

Probabilities represented pictorially.

Probability Experiments

A chance process that leads to a well-defined results called outcomes.

Tree Diagram

A device consisting of line segments emanating from a starting point and also from the outcome point. It is used to determine all possible outcomes in a probability experiment.

Event

An event consist of a set of outcomes of a probability experiment.

Simple Event

An event with one outcome.

Equally Likely Events

Are events that have the same probability of occurring.

Probability

As a general concept can be defined as the chance of an event occurring

Classical Probability

Assumes that all outcomes in the sample space are equally likely to occur.

Probability Rule #2

If an event E cannot occur (i.e., the event contains no members in the sample space), its probability is 0.

Law of Large Numbers

If the empirical probability of getting a head is computed by using a small number oftrials, it is usually not exactly . However, as the number of trials increases, the empirical probability of getting a head will approach the theoretical probability of , if in fact the coin is fair (i.e., balanced).

Probability Rule #3

If the event E is certain than the probability is 1.

Rules for Complimentary Events (Definition)

If the probability of an event or the probability of its complement is known, then the other can be found by subtracting the probability from 1.

Sample Space

In an experiment, this is the set of all possible outcomes of a probability experiment.

Complimentary 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 "E bar".

Empirical Probability (Formula)

P(E) = [Frequency of Class]/[Total Frequencies in Distribution] = [f] / [n]

Empirical Probability (Definition)

Relies on actual experience to determine the likelihood of outcomes.

Probability Rule #1

The probability of any event E is a number (either a fraction or decimal) between and including 0 and 1. This is denoted by 0 ≤ P(E ) ≤ 1.

Outcomes

The result of a single trial of a probability experiment.

Probability Rule #4

The sum of the probabilities of all the outcomes in the sample space is 1.

Compound Event

Two or more outcomes or simple events.

Subjective Probability

Uses a probability value based on an educated guess or estimate, employing opinions and inexact information.

Rules for Complimentary Events (Formula)

[P(E bar) = 1 - P(E )] or [P(E ) 1 - P(E bar)] or [P(E ) + P(E bar) = 1].