Page 42 - Applied statistics and probability for engineers

20 Chapter 2/Probability

Transmission
Automatic Manual

Sunroof
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 48 outcomes in the sample space.

Example 2-5 Automobile Colors Consider an extension of the automobile manufacturer illustration in
the previous example in which another vehicle option is the interior color. There are four
choices of interior color: red, black, blue, or brown. However,
r With a red exterior, only a black or red interior can be chosen.
r With a white exterior, any interior color can be chosen.
r With a blue exterior, only a black, red, or blue interior can be chosen.
r 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 extended to show that there are 120 different vehicle
types in the sample space.
Exterior color Red White Blue Brown

Interior color Black Red
12 3 2 = 24 12 3 4 = 48 12 3 3 = 36 12 3 1 = 12
24 + 48 + 36 + 12 = 120 vehicle types
FIGURE 2-7 Tree diagram for different types of vehicles with interior colors

2-1.3 EVENTS
Often we are interested in a collection of related outcomes from a random experiment. Related
outcomes can be described by subsets of the sample space, and set operations can also be applied.
Event
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
complements to form other events of interest. Some of the basic set operations are summarized
here in terms of events: