Applied Statistics and Probability for Engineers

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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