CH 5

Tree Diagram

A graph that is helpful in organizing calculations that involve several stages. Each segment in the tree is one stage of the problem. The branches of a tree diagram are weighted by probabilities.

Outcome

A particular result of an experiment.

Joint Probability

A probability that measures the likelihood two or more events will happen concurrently.

Experiment

A process that leads to the occurrence of one and only one of several possible observations.

POSTERIOR PROBABILITY

A revised probability based on additional information.

CONTINGENCY TABLE

A table used to classify sample observations according to two or more identifiable characteristics.

Probability

A value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur.

Collectively exhaustive

At least one of the events must occur when an experiment is conducted

Classical probability

Based on the assumption that the outcomes of an experiment are equally likely. Using the classical viewpoint, the probability of an event happening is computed by dividing the number of favorable outcomes by the number of possible outcomes.

MULTIPLICATION FORMULA

If there are m ways of doing one thing and n ways of doing another thing, there are ways of doing both. m * n In terms of a formula: Total number of arrangements = (m)(n)

Bayes Theorem

It is designed to find the probability of one event, A, occurring, given that another event, B, has already occurred.

Law of Large Numbers

Over a large number of trials, the empirical probability of an event will approach its true probability.

GENERAL RULE OF MULTIPLICATION

P(A and B) = P(A) * P(B | A)

SPECIAL RULE OF MULTIPLICATION

P(A and B) = P(A) * P(B)

SPECIAL RULE OF ADDITION

P(A or B) = P(A) + P(B)

GENERAL RULE OF ADDITION

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

Complement Rule

P(A) = 1 - P(~A) This is the complement rule. It is used to determine the probability of an event occurring by subtracting the probability of the event not occurring from 1.

COMBINATION FORMULA

The formula to count the number of r object combinations from a set of n objects is: nCr = n! / r!(n r)!

PRIOR PROBABILITY

The initial probability based on the present level of information.

Independence

The occurrence of one event has no effect on the probability of the occurrence of another event.

Mutually exclusive

The occurrence of one event means that none of the other events can occur at the same time.

PERMUTATION FORMULA

The permutation formula is applied to find the possible number of arrangements when there is only one group of objects. nPr = n! / (n - r)!

Event

A collection of one or more outcomes of an experiment

Subjective Concept of Probability

The likelihood (probability) of a particular event happening that is assigned by an individual based on whatever information is available.

Conditional Probability

The probability of a particular event occurring, given that another event has occurred.

Empirical probability

The probability of an event happening is the fraction of the time similar events happened in the past.