23 terms

Chance experiment

Any process that generates observations whose outcomes cannot be predicted with certainty

Sample space

Set of all possible outcomes of a chance experiment

Event

An outcome or set of outcomes of a chance experiment

Simple event

An event that consists of exactly one outcome

Complement

An event that contains the set or outcomes not included by a second event;

Find the complement by subtracting

Complement = 1 - probability(event)

Find the complement by subtracting

Complement = 1 - probability(event)

Intersection

The set of all elements that are common to 2 or more sets.

Union

Set of all elements that are contained in 2 or more sets

Venn Diagram

A diagram that uses circles to display elements of different sets; overlapping circles show common elements

Disjoint

Two non-overlapping sets; aka mutually exclusive events

Mutually exclusive

Events that cannot happen at the same time

Probability of an event

Number of favorable outcomes divided by the total number of possible outcomes

Law of large numbers

As the number of repetitions of a probability experiment increases, the empirical probability (the proportion with which a certain outcome is observed) gets closer to the theoretical probability of the outcome

general addition rule

For any two events, A and B, the probability of A OR B is the probability of A and B minus their joint probability

P(A U B) = P(A) + P(B) - P(A and B)

P(A U B) = P(A) + P(B) - P(A and B)

General Multiplication Rule for Any Two Events

For any two events, A and B, the probability of A and B is the probability of A times the probability of B occurring given that A has occurred

Independent Events

Two or more events for which the outcome of one event does not affect the probability of the other; P(A) = P(A | B)

Dependent Events

Two or more events in which the occurrence of one event affects the probability of the other events; do not always possess a cause-and-effect relationship

Sampling without replacement

Removes each selected element from the population before the next selection is made to guarantee no element appears more than once in a single sample; probability of selecting any outcome changes after each selection

Sampling with replacement

Once an element has been included in the sample, it is returned to the population and may be selected again; probability of selecting any outcome remains constant

10% sampling condition

When sampling without replacement, the change in the probability of an outcome can be regarded as insignificant and thus ignored when sampling less than 10% of a population

Conditional Probability

Probability of an event occurring given that another event is known to have occurred; denoted as P(A | B)

Empirical probability

Probability that is based on simulation, experimentation or testing; the relative frequency of a successful outcome among those trials

Simulation

Modeling a problem situation or event that would be too difficult or impractical to actually perform; often used to calculate empirical probabilities

Table of Random Digits

Long string of digits (0 to 9) where the digits are independent of each other (knowing one digit does not give any knowledge to predicting another digit) and where any digit (0 to 9) has an equal chance of occurring as the next digit; used for probability simulations, random selection and random assignment