STAT 3021
Chapter 2. Probability
2.1, 2.2 Sample Space and Events
Definition 1.
The set of all possible outcomes of a statistical experiment is called the
sample space
and
is represented by the symbol
S
.
Example 1.
a. Rolling a die and observe the number it shows on the top face. Then
S
=
{
1
,
2
,
3
,
4
,
5
,
6
}
b. Rolling two dice and observe the two numbers they show. Then
S
=
{
(1
,
1)
,
(1
,
2)
,
(1
,
3)
, ...
(6
,
5)
,
(6
,
6)
}
c. Rolling two dice and calculate the sum of the two numbers. Then
S
=
{
2
,
3
,
4
,
5
,
6
, ...,
12
}
Example 2.
Suppose that we randomly select a student from class and ask a question.
In the below
situation, describe the sample space for the experiment.
a. How much time (in hours) did the student spend studying during the last 24 hours?
S
= [0
,
20]
b. In what state was the student born, given that he/she was born in the U.S.?
S
=
{
AL, AK, AZ, ..., WY
}
c. How many friends does the student have?
S
=
{
0
,
1
, ...
}
In some experiment it is helpful to list the elements of the sample space systemically by means of a tree
diagram.
Example 3.
An experiment consists of flipping a coin and then flipping it a second time if a head occurs.
If a tail occurs on the first flip, then a die is tossed once. To list the elements of the sample space providing
the most information, we construct the tree diagram below.
Hence
S
=
{
HH, HT, T
1
, T
2
, T
3
, T
4
, T
5
, T
6
}
1