QMB 2100 - (Chapter 5: A Survey of Probability Concepts)

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 results.

POSTERIOR PROBABILITY

A revised probability based on additional information.

CONTINGENCY TABLE

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

Probability

A value between 0 and 1 inclusive that represents the likelihood a particular event happens.

COLLECTIVELY EXHAUSTIVE

At least one of the events must occur when an experiment is conducted. all your options multiple options to choose from

LAW OF LARGE NUMBERS

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

Special rule of multiplication

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

General rule of multiplication

P(A and B) = P(A)P(B|A) The ___________________ refers to events that are not independent A conditional probability is the likelihood an event will happen, given that another event has already happened

Special Rule of Addition

P(A or B) = P(A) + P(B) The ___________________ refer to the probability that any two or more events can occur The ___________________ is used when the events are mutually exclusive

General Rule of Addition

P(A or B) = P(A) + P(B) - P(A and B) The ___________________ is used when the events are not mutually exclusive

The Complement Rule

P(A) = 1 - P(~A) The ___________________ is used to determine the probability of an event happening by subtracting the probability of an event not happening

Event

A collection of one or more outcomes of an experiment.

PRIOR PROBABILITY

The initial probability based on the present level of information.

Subjective Probability

The likelihood (probability) of a particular event happening that is assigned by an individual based on whatever information is available. based on knowledge and past history ex Estimating the likelihood the New England Patriots will be in the Super Bowl next year Estimating the likelihood the U.S. budget deficit will be reduced by half in the next 10 years

INDEPENDENCE

The occurrence of one event has no effect on the probability of the occurrence of another event. -what happens the 1st time won't happen the next time

MUTUALLY EXCLUSIVE

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

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. Probability of a successful flight = # of successful flights / Total # of flights -the more occurrence the more accurate it will be

Bayes' Theorem

is a method of revising a probability, given that additional information is obtained For two mutually exclusive and collectively exhaustive events

The Combination Formula

nCr = n!/r!(n-r)! Another counting formula useful in determining the total number of outcomes A combination is an arrangement where the order of the objects selected is not important n=total # r= # selected

Permutation Formula

nPr = n!/(n-r)! Any arrangement of r objects selected from a single group of n possible objects. order is important n=total # r= # selected

Classical Probability

probability of an event = number of favorable outcomes/ total number of possible outcomes