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Chapter 7: Probability
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Sample Space
When we toss a coin, we have two possible outcomes – a head (
H
) or a tail
(
T
). We can summarize these possible outcomes by using set notation such
as {
H
,
T
}. When a child is born, the gender of the child is either a boy (
B
)
or a girl (
G
). Here we can summarize the possible outcomes again by using
set notation such as {
B
,
G
}. If we consider randomly selecting two items
from a production line and if we let
D
represents a defective item and
N
represents a non-defective item, then using set notation, the possible
outcomes can be summarized by {
DD
,
DN
,
ND
,
NN
}. In each case, the
outcomes enclosed in {}, lists
all
the possible outcomes. Such a complete
list is called a
sample space
.
Definition: Sample Space
The sample space for a random experiment is the list or set of all
possible outcomes for the experiment.
Example 7-1:
A fair regular six-sided die is rolled with faces numbered 1
to 6. List the sample space for this random experiment.
Solution:
Let
S
represent the sample space. Then
S
= {1, 2, 3, 4, 5, 6}.
Example 7.2:
List the sample space for a two-child family.
Solution:
Let
B
represent the outcome of a boy and
G
for a girl. The
diagram in
Figure 7-1
, called a
tree diagram
, depicts all the possible
outcomes.