http://www.ck12.org Chapter 3. An Introduction to Probability
that there are four possible outcomes for each toss. In other words, the simple events areHH,HT,T H,andT T. The
table below shows all the possible outcomes.
H T
H HH HT
T T H T T
Figure:The possible outcomes of flipping two coins.
What we have accomplished so far is a listing of all the possible simple events of an experiment. This collection is
called thesample spaceof an experiment.
Sample Space
The set of all possible outcomes of an experiment, or the collection of all the possible simple events of an experiment.
We will denote a sample space byS.
Example:
Experiment: We want to investigate the sample space of throwing a die and the sample space of tossing a coin.
Solution:
As we know, there are 6 possible outcomes for throwing a die. We may get 1, 2 , 3 , 4 , 5 ,or 6. So we write the sample
space as the set of all possible outcomes:
S={ 1 , 2 , 3 , 4 , 5 , 6 }
Similarly, the sample space of tossing a coin is either head(H)or tail(T)so we writeS={H,T}.
Example:
Experiment: Suppose a box contains three balls, one red, one blue and one white. One ball is selected, its color is
observed, and then the ball is placed back in the box. The balls are scrambled and again a ball is selected and its
color is observed. What is the sample space of the experiment?
Solution:
It is probably best if we draw a diagram to illustrate all the possible drawings.