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More Sample Spaces and Set Notation Examples
Example 1
Roll 2 dies, one after the other, and record the roll of the Frst die and then the roll of the second die, a possible
outcome is an ordered pair of two numbers and the sample space is
Ω
1
=
(1
,
1)
,
(1
,
2)
...
(1
,
6)
(2
,
1)
,
(2
,
2)
...
(2
,
6)
.
.
.
.
.
.
.
.
.
.
.
.
(6
,
1)
,
(6
,
2)
...
(6
,
6)
±or this sample space, the order of the rolls matters  this gives us 36 elementary events, all of which have the
same probability of occurring.
Example 2
Alternatively, we could just record the outcomes of rolling the two dies at the same time. An outcome then has
the form of a set of two numbers (in a set, the order of the elements does not matter, i.e. we can rearrange them
freely). This leads us to a slightly di²erent sample space:
Ω
2
=
{
1
,
1
}
,
{
1
,
2
}
...
{
1
,
6
}
{
2
,
2
}
...
{
2
,
6
}
.
.
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This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.
 Spring '11
 Zhou

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