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35 Cards in this Set
 Front
 Back
probability

the chance of an event occurring


probability experiment

a chance process that leads to well defined results called outcomes


outcome

the result of a single trial of a probability experiment


sample space

the set of all possible outcomes of a probability experiment


event

a set of outcomes of a probability experiment


simple event

event with one outcome


compound event

consists of two or more outcomes or simple events


the three basic interpretations of probability

1) classical probability
2)empirical or relative frequency probability 3)subjective probability 

classical probability assumes...

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


formula for classical probability

the probability of any event "E" is
(number of outcomes divided in E)/ (total number of outcomes in sample space) 

in what ways can probabilities be expressed?

as fraction, decimals and sometimes percentages


rounding rule for probabilities

should be expressed as reduced fractions or rounded to two or three decimal places
for very small probability round to the nearest non zero .0000578=.00006 

four basic probability rules

The sum of probabilities of the outcome in a sample space it 1.
If an event "E" is certain, the probability of "E" is 1. If an event "E" cannot occur, the probability is 0. The probability of event "E" is between and including 0 and 1. 

the complement of event "E" is shown by...

E "bar"


Venn diagrams represent

probabilities pictorially


empirical probability

relies on actual experience or observation to determine the likelihood of outcomes


Formula for empirical probability

f/n
where f=frequency for class n=total frequencies in the distribution 

the law of large numbers

as the number of trials increase the empirical probability will approach the theoretical probability


subjective probability

uses opinions and inexact information
(educated guesses) 

mutually exclusive events

cannet occur at the same time, they have no outcomes in common


when "A" and "B" are mutually exclusive the probability that "A" or "B" will occur is

P(A)+P(B)


when "A" and "b" are NOT mutually exclusive the probability is found by

P(A)+P(B)P(A and B)


independent events

do not effect the probability of another event occurring


rule for two independent events both occurring

P(A)+P(B)


dependent events

if the outcome or occurrence of one event effects the outcome or occurrence of another


for dependent events the probability of both occurring is

P(A)*P(B/A)


conditional probability

the probability of event "B" occurring after event "A"


formula for conditional probability

P(A and B)/P(A)


0!=

1


permutation

an arrangement of objects in a specific order


Permutation rule

nPr = n!/(nr)!
n= objects r= objects at a time 

combination

selection of objects without regard to order


combinations are used when

the order of arrangement is not important


combination rule

nCr = n!/(nr)!r!
n= objects r= objects at a time 

fundamental counting rule (define)

the number of ways a sequence of "n" events can occur if the first event can occur K 1 ways, the second can occur K 2 ways, etc.
