3.1. Events, Sample Spaces, and Probability http://www.ck12.org
As you can see from the diagram, it is possible that you will get the red ballRon the first drawing and then another
red one on the second,RR.You can also get a red one on the first and a blue on the second and so on. From the
diagram above, we can see that the sample space is:
S={RR,RB,RW,BR,BB,BW,W R,W R,WW}
Each pair in the set above gives the first and second drawings, respectively. That is,RWis different fromW R.
We can also represent all the possible drawings by a table or a matrix:
R B W
R RR RB RW
B BR BB BW
W W R W B WW
Figure:Table representing the possible outcomes diagrammed in the previous figure
Where the first column represents the first drawing and the first row represents the second drawing.
Example:
Experiment: Consider the same experiment as in the example before last but this time we will draw one ball and
record its color but we will not place it back into the box. We will then select another ball from the box and record
its color. What is the sample space in this case?
Solution:
The diagram below illustrates this case:
You can clearly notice that when we draw, say, a red ball, there will remain blue and white balls. So on the second
selection, we will either get a blue or a while ball. The sample space in this case is: