Stats: Introduction to Probability
Sample Spaces
A sample space is the set of all possible outcomes. However, some sample spaces are better than others.
Consider the experiment of flipping two coins. It is possible to get 0 heads, 1 head, or 2 heads. Thus, the
sample space could be {0, 1, 2}. Another way to look at it is flip { HH, HT, TH, TT }. The second way
is better because each event is as equally likely to occur as any other.
When writing the sample space, it is highly desirable to have events which are equally likely.
Another example is rolling two dice. The sums are { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }. However, each of
these aren't equally likely. The only way to get a sum 2 is to roll a 1 on both dice, but you can get a sum
of 4 by rolling a 1-3, 2-2, or 3-1. The following table illustrates a better sample space for the sum obtain
when rolling two dice.
Classical Probability
The above table lends itself to describing data another way -- using a probability distribution. Let's
consider the frequency distribution for the above sums.
First Die
Second Die
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3
4
5
6
7
8
9
4
5
6
7
8
9
10
5
6
7
8
9
10
11
6
7
8
9
10
11
12
Sum
Frequency
Relative
Frequency
2
1
1/36
3
2
2/36
4
3
3/36
5
4
4/36
Page 1 of 3
Stats: Introduction to Probability
8/20/2011
http://people.richland.edu/james/lecture/m170/ch05-int.html