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We use tree diagrams, Venn diagrams and
graphs to represent sample
spaces.
Tree Diagrams
A tree diagram enables us to find the elements of the sample
space.
E.g. If an experiment's
trial involves tossing a fair coin, then
the possible outcomes are head and tail. This information can be
depicted in the following tree diagram.
Clearly, S = {H, T}
Recall that each element of the sample
space is called a sample
point. So, the sample points are H and T.
Consider the experiment of tossing a coin twice where we are interested
in the number of heads. The tree diagram is shown below.
Note that the tree diagram representation of this experiment involves
two parts, 'the first toss of the coin' and 'the second toss of the coin'.
Venn Diagrams
The sample space and an event may be represented on a
Venn diagram.
For the experiment of tossing a fair coin, the possible
outcomes are
head and tail. So, the following Venn diagram represents the
experiment's sample space.
If A is the event 'a head falls', then we can use the following
Venn diagram to represent it.
Graphical Representation
If an experiment's trial
involves rolling a die twice, then there are
36 elements in the sample space
as shown below.
As the tree diagram will be very large, the following simple graphical
representation can be used instead.
Key Terms
tree diagram, Venn diagram, graphical
representation
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