Chapter 4. Introduction to Probability
QBA 237 Basic Business Statistics
Raju Mainali
Summer 2020

Outline
4.1
Random Experiments, Counting Rules, and Assigning
Probabilities
4.2
Events and Their Probabilities
4.3
Some Basic Relationship of Probability
4.4
Conditional Probability
1

Basic Ideas
I
An
experiment
is a process of making an observation when
there is uncertainty about which of two or more possible
outcomes will result.
Experiment
Experiment Outcomes
Tossing a coin
Head, tail
Rolling a die
1,2,3,4,5,6
Inspection a part
Defective, non-defective
Play a football game
Win, lose, tie
I
The set of
all possible outcomes
of an experiment is called the
sample space
for the experiment. The sample space is
denoted as
S
.
2

Example 1
I
Find a sample space of throwing a die.
S
=
{
1
,
2
,
3
,
4
,
5
,
6
}
I
Find a sample space of tossing a coin.
S
=
{
H
,
T
}
I
Find a sample space of tossing two coins simultaneously.
S
=
{
HH
,
HT
,
TT
}
(
HT
=
TH
)
I
Find a sample space of tossing two coins in turn.
S
=
{
HH
,
HT
,
TH
,
TT
}
(
HT
6
=
TH
)
3

Example 1 (cont’d)
I
Suppose a box contains three balls,
one red, one blue, and one
white
. One ball is selected, its color is observed, and then the
ball is placed back in the box. The balls are scrambled, and
again, a ball is selected and its color is observed. What is the
sample space of the experiment?
S
=
{
RR
,
RB
,
RW
,
BR
,
BB
,
BW
,
WR
,
WB
,
WW
}
4

Counting Methods
When computing probabilities, it is sometimes necessary to
determine the number of outcomes.
For example, a car is available in any of three colors: red, blue, or
green, and comes with either a large or small engine.
In how many ways can a buyer choose a car?
S
=
{
(R, L), (R, S), (B, L), (B, S), (G, L), (G, S)
}
.
The total number of choices is 6.
5

Fundamental Principle of Counting
In a sequence of
n
events in which the first one has
k
1
possibilities
and the second event has
k
2
and the third has
k
3
, and so forth, the
total number of possibilities of the sequence will be
k
1
×
k
2
× · · · ×
k
n
Example
) A restaurant offers a special dinner menu every day.
There are
ten entrees, eight appetizers, and seven desserts
to
choose from. A customer can only select one item from each
category. How many different meals can be ordered from the
special dinner menu?
6

Permutations
A
permutation
is an arrangement of
n
objects
in a specific order
.

#### You've reached the end of your free preview.

Want to read all 31 pages?

- Spring '14
- Danepeterson
- Conditional Probability, Probability, Probability theory