Page 37 - Probability Demystified

P. 37

26 CHAPTER 2 Sample Spaces

EXAMPLE: A box contains a red ball (R), a blue ball (B), and a yellow ball
(Y). Two balls are selected at random in succession. Draw a tree diagram and
ﬁnd the sample space if the ﬁrst ball is replaced before the second ball is
selected.

SOLUTION:
There are three ways to select the ﬁrst ball. They are a red ball, a blue ball, or
a yellow ball. Since the ﬁrst ball is replaced before the second one is selected,
there are three ways to select the second ball. They are a red ball, a blue ball,
or a yellow ball. The tree diagram is shown in Figure 2-3.

Fig. 2-3.

The sample space consists of nine outcomes. They are RR, RB, RY, BR,
1
BB, BY, YR, YB, YY. Each outcome has a probability of :
9
Now what happens if the ﬁrst ball is not replaced before the second ball
is selected?
EXAMPLE: A box contains a red ball (R), a blue ball (B), and a yellow ball
(Y). Two balls are selected at random in succession. Draw a tree diagram and
ﬁnd the sample space if the ﬁrst ball is not replaced before the second ball is
selected.

SOLUTION:
There are three outcomes for the ﬁrst ball. They are a red ball, a blue ball, or
a yellow ball. Since the ﬁrst ball is not replaced before the second ball is
drawn, there are only two outcomes for the second ball, and these outcomes
depend on the color of the ﬁrst ball selected. If the ﬁrst ball selected is blue,
then the second ball can be either red or yellow, etc. The tree diagram is
shown in Figure 2-4.

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