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Lecture 2
Introduction to Probability
Source:
/1
/
D.R.Anderson, D.J.Sweeney, T.A.Williams. Quantitative Methods for Business, SouthWestern
College Publishing, 11th edition.
Chapter 2.
Contents:
2.1
Experiments and the sample space
2.2
Assigning probabilities to experimental outcomes
2.3
Events and their probabilities
2.4
Some basic relationships of probability
Business decisions are often based on an analysis of uncertainties such as the following:
1. What are the "chances" that sales will decrease if we increase prices?
2. What is the "likelihood" that а new assembly method will increase productivity?
3. How “likely’’ is it that the project will be completed on time?
4. What are the "odds" in favor of
а new investment being profitable?
Probability is а numerical measure of the likelihood that an event will occur. Thus, probabilities could be used as
measures of the
degree
of uncertainty
associated with the four events previously listed. If probabi1ities were available, we could determine the likelihood of each
event occurring.
Probability values are always assigned on а scale from 0 to 1. А probability near 0 indicates that an event is unlikely to occur; а
probability near 1 indicates that an event is almost certain to occur. Other probabilities between 0 and 1 represent varying degrees of
likelihood that an event will occur.
Probability is important in decision making because it provides а way to measure, express, and ana1yze the uncertainties associated with
future events.
2.1
Experiments
and the Sample space
Experiment
is a process that generates welldefined
outcomes
.
(On any single repetition of an
experiment
one and only one
of possible experimental outcomes will occur)
The set of
all
possible experimental outcomes is called the
Sample Space
.
Particular experimental outcome is called the
Sample Point (
or
Simple Event)
Sample Point (
or
Simple Event)
can not be decomposed into a simpler
outcome.
Examples 2.1
:
Experiment
Sample space
i
E
are experimental outcomes(sample points)
1.
Tossing 1 coin
{
}
2
1
,
E
E
where
1
E
→
Head (H),
2
E
→
Tail (T)
1
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Tossing 3 coins at once
where
{ }
THH
HTT
HTH
THT
HHT
TTH
TTT
HHH
,
,
,
,
,
,
,
8
4
7
3
6
2
5
1
8
7
6
5
4
3
2
1
→
→
→
→
→
→
→
→
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
E
3.
Rolling a fair die
where
{
}
6
3
5
2
4
1
,
,
,
,
,
6
3
5
2
4
1
6
5
4
3
2
1
→
→
→
→
→
→
E
E
E
E
E
E
E
E
E
E
E
E
4.
Conducting a sales call
{
}
2
1
,
E
E
where
1
E
 the customer purchases the product,
2
E
 the customer does not purchase the
product.
2.2
Assigning probabilities to experimental outcomes
The probability of an experimental outcome is a numerical measure of the likelihood that the
experimental outcome will occur.
How probabilities for the experimental outcomes can be determined?
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 Spring '11
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