Definitions
•
Probability experiment
 An action, or trial,
through which specific results (counts,
measurements, or responses) are obtained.
•
Outcome
 The result of a single trial in a
probability experiment.
•
Sample Space
 The set of all possible
outcomes of a probability experiment.
•
Event
 Consists of one or more outcomes and
is a subset of the sample space.
•
Simple event
 An event that consists of a
single outcome (An event that consists of more
than one outcome is not a simple event).
•
Fundamental Counting Principle
 If one
event can occur in
m
ways and a second event
can occur in
n
ways, the number of ways the
two events can occur in sequence is
m*n
.
Can
be extended for any number of events occurring
in sequence.
•
Law of Large Numbers
 As an experiment is
repeated over and over, the empirical
probability of an event approaches the
theoretical (actual) probability of the event.
•
Subjective Probability
 Intuition, educated
guesses, and estimates.
•
Range of probabilities rule
 The probability of
an event
E
is between 0 and 1, inclusive.
0 ≤
P(E)
≤ 1
•
Complement of event
E (E')

The set of all
outcomes in a sample space that are not
included in event
E
.
Denoted
E
′ (
E
prime).
P
(
E
′) +
P
(
E
) = 1
•
Permutation
 An ordered arrangement of
objects. The number of different permutations of
n
distinct objects is
n
! (
n
factorial).
n
! =
n
∙(
n
–
1)∙(
n
– 2)∙(
n
– 3)∙ ∙ ∙3∙2 ∙1;
0! = 1
n
P
r
Ex
There are 15 dogs entered in a show.
How
many ways can first, second, and third place be
awarded?
N=15
R=3
15
P
3
15!/(133)!= 3,730 ways
•
Combination of
n
objects taken
r
at a time 
A
selection of
r
objects from a group of
n
objects
without regard to order
n
C
r
Ex
There are 13 students in a club.
How many
ways can four students be selected to attend a
conference?
N=13
R=4
13
C
4
13!/(134)!
(4!)= 715 ways
Formulas
Classical (theoretical) Probability 
Each
outcome in a sample space is equally likely.
Empirical (statistical) Probability 
Based on
observations obtained from probability experiments.
The relative frequency of an event.
4!
(4*3*2*1)=24
How many 4 letter TV call signs are possible, if
each sign must start with either a K or W?
1
st
letter=2 (K or W)
2
nd
letter=26
3
rd
letter=26
4
th
letter=26
2*26*26*26=35,152 possibilities.
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 Fall '10
 Raney
 Normal Distribution, Probability, standard normal table, Probability The Probability

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