22 CHAPTER 2 PROBABILITY
With a blue exterior, only a black, red, or blue interior can be chosen.
With a brown exterior, only a brown interior can be chosen.
In Fig. 2-6, there are 12 vehicle types with each exterior color, but the number of interior
color choices depends on the exterior color. As shown in Fig. 2-7, the tree diagram can be ex-
tended to show that there are 120 different vehicle types in the sample space.
2-1.3 Events
Often we are interested in a collection of related outcomes from a random experiment.
Color
Stereo
Air conditioning
Transmission
Automatic Manual
123 123 123 123
Yes No Yes No
n = 48
Figure 2-6 Tree diagram for different types of vehicles.
Exterior color Red White Blue Brown
Interior color Black Red
12 × 2 = 24 12 × 4 = 48 12 × 3 = 36 12 × 1 = 12
24 + 48 + 36 + 12 = 120 vehicle types
Figure 2-7 Tree dia-
gram for different
types of vehicles with
interior colors.
We can also be interested in describing new events from combinations of existing events.
Because events are subsets, we can use basic set operations such as unions, intersections, and
An eventis a subset of the sample space of a random experiment.
Definition
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