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22 CHAPTER 2 PROBABILITY

Transmission
Manual
Automatic
Air conditioning
n = 48
Yes No Yes No

Stereo

1 2 3 1 2 3 1 2 3 1 2 3
Color

Figure 2-6 Tree diagram for different types of vehicles.

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.

Definition
An event is a subset of the sample space of a random experiment.

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

Exterior color Red White Blue Brown

Interior color Black Red
Figure 2-7 Tree dia-
gram for different
12 × 2 = 24 12 × 4 = 48 12 × 3 = 36 12 × 1 = 12
types of vehicles with
interior colors. 24 + 48 + 36 + 12 = 120 vehicle types