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