Ch. 5:
(Probability)
5.1
(Definition)
 an experiment (
):

a trial (
):

a basic outcome / an elementary event / a simple event / a sample point(
/
):
. (ex) a, b, e1, e2, etc.

a sample space (
):
S
.
 An event or outcome (
/
):
. (ex) A, E, F, W, E1, E2, etc, and we write E
S, a
F, etc.
0
1
: (
Probability
is a measure, on a scale of zero to one, inclusive, of the chance of occurrence of an event, as
determined by applying the appropriate choice from the following four definitions of probability:)
5.2
Classical definition of probability(
)
 Suppose that an experiment can result in a finite number
n
of equally likely outcomes, and that
k
of these outcomes
comprises a particular event
E
. Then
the probability of event E
, denoted by
P(E)
, is the ratio
k/n
, where 0
k/n
1, and
we write
P(E) = k/n
. The classical definition is useful for many of our business related problems, but it cannot be used
where there is an infinite number of possible outcomes or where the outcomes are not equally likely. Hence we need also
the historically second definition:

.
2,
4, 6
E
P(E) = k/n = 3/6
.
Relative Frequency definition of probability(
)
 If an event
A
occurs
a
times in
m
repetitions of an experiment,
m
A
is called
the (absolute) frequency
of event
A
,
m
A
/m
is called
the relative frequency
of event
A
, and we have 0
m
A
/m
1. For smaller values of m, the values of
m
A
/m
fluctuate considerably, but for larger values of
m
,
m
A
/m
tends to stabilize about a specific number,
P(A)
, called the
probability of event
A
, which is the limiting value of
m
A
/m
as
m
increases. Then for a larger values of
m
we may say
P(A)
=
m
A
/m
. The frequency definition of probability can be used to solve some of our business problems that the classical