Applied Statistics and Probability for Engineers

26 CHAPTER 2 PROBABILITY

2-19. Three events are shown on the Venn diagram in the

following figure:

Reproduce the figure and shade the region that corresponds to

each of the following events.

(a) (b)

(c) (d)

(e)

2-20. Three events are shown on the Venn diagram in the

following figure:

Reproduce the figure and shade the region that corresponds to

each of the following events.

(a) (b)

(c) (d)

(e)

2-21. A digital scale is used that provides weights to the

nearest gram.

(a) What is the sample space for this experiment?

Let Adenote the event that a weight exceeds 11 grams, let B

denote the event that a weight is less than or equal to 15

grams, and let Cdenote the event that a weight is greater than

or equal to 8 grams and less than 12 grams.

Describe the following events.

(b) (c)

(d) (e)

(f) (g)

(h) (i)

2-22. In an injection-molding operation, the length and

width, denoted as Xand Y, respectively, of each molded part

are evaluated. Let

Adenote the event of 48 X 52 centimeters

Bdenote the event of 9 Y 11 centimeters

Cdenote the event that a critical length meets customer

requirements.

Construct a Venn diagram that includes these events. Shade

the areas that represent the following:

(a)A (b)

(c) (d)

(e) If these events were mutually exclusive, how successful

would this production operation be? Would the process

produce parts with X50 centimeters and Y 10

centimeters?

2-23. Four bits are transmitted over a digital communica-

tions channel. Each bit is either distorted or received without

distortion. Let Ai denote the event that the ith bit is distorted,

.

(a) Describe the sample space for this experiment.

(b) Are the Ai’s mutually exclusive?

Describe the outcomes in each of the following events:

(c) (d)

(e) (f)

2-24. A sample of three calculators is selected from a manu-

facturing line, and each calculator is classified as either defective

or acceptable. Let A, B, and Cdenote the events that the first,

second, and third calculators respectively, are defective.

(a) Describe the sample space for this experiment with a tree

diagram.

Use the tree diagram to describe each of the following

events:

(b)A (c)B

(d) (e)

2-25. A wireless garage door opener has a code determined

by the up or down setting of 12 switches. How many out-

comes are in the sample space of possible codes?

2-26. Disks of polycarbonate plastic from a supplier are an-

alyzed for scratch and shock resistance. The results from 100

disks are summarized below:

shock resistance

high low

scratch high 70 9

resistance low 16 5

Let Adenote the event that a disk has high shock resistance,

and let Bdenote the event that a disk has high scratch

A ̈B B ́C

A 1 ̈A 2 ̈A 3 ̈A 4 1 A 1 ̈A 22 ́ 1 A 3 ̈A 42

A 1 A 1 ¿

i1,p, 4

A¿ ́B A ́B

A ̈B

B¿ ̈C A ́ 1 B ̈C 2

1 A ́C 2 ¿ A ̈B ̈C

A¿ A ́B ́C

A ́B A ̈B

1 A ̈B 2 ¿ ́C

1 A ̈B 2 ́C 1 B ́C 2 ¿

A¿ 1 A ̈B 2 ́ 1 A ̈B¿ 2

AB

C

1 A ̈B 2 ¿ ́C

1 A ̈B 2 ́C 1 B ́C 2 ¿

A¿ A ̈B

AB

C

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