Applied Statistics and Probability for Engineers

36 CHAPTER 2 PROBABILITY

probability is the sum of any collection of mutually exclusive events with union equal to the

same range for X. One example is

Another example is

The best choice depends on the particular probabilities available.

EXERCISES FOR SECTION 2-3

P 1 7.1X7.4 2 P 1 7.4X7.8 2

P 1 6.5X7.8 2 P 1 6.5X6.6 2 P 1 6.6X7.1 2

P 1 6.5X7.8 2 P 1 6.5X7.0 2 P 1 7.0X7.5 2 P 1 7.5X7.8 2

2-49. If , and

determine the following probabilities:

(a) (b)

(c) (d)

(e) (f )

2-50. If A,B, and Care mutually exclusive events with

and determine the fol-

lowing probabilities:

(a) (b)

(c) (d)

(e)

2-51. If A,B, and Care mutually exclusive events, is it pos-

sible for P(A) 0.3, P(B) 0.4, and P(C) 0.5? Why or

why not?

2-52. Disks of polycarbonate plastic from a supplier are an-

alyzed for scratch and shock resistance. The results from 100

disks are summarized as follows:

shock resistance

high low

scratch high 70 9

resistance low 16 5

(a) If a disk is selected at random, what is the probability that

its scratch resistance is high and its shock resistance is

high?

(b) If a disk is selected at random, what is the probability

that its scratch resistance is high or its shock resistance

is high?

(c) Consider the event that a disk has high scratch resistance

and the event that a disk has high shock resistance. Are

these two events mutually exclusive?

2-53. The analysis of shafts for a compressor is summarized

by conformance to specifications.

roundness conforms

yes no

surface finish yes 345 5

conforms no 12 8

P 1 A¿ ̈B¿ ̈C¿ 2

P 1 A ̈B 2 P 31 A ́B 2 ̈C 4

P 1 A ́B ́C 2 P 1 A ̈B ̈C 2

P 1 A 2 0.2,P 1 B 2 0.3, P 1 C 2 0.4,

P 31 A ́B 2 ¿ 4 P 1 A¿ ́B 2

P 1 A¿ ̈B 2 P 1 A ̈B¿ 2

P 1 A¿ 2 P 1 A ́B 2

P 1 A 2 0.3 P 1 B 2 0.2, P 1 A ̈B 2 0.1, (a) If a shaft is selected at random, what is the probability that

the shaft conforms to surface finish requirements?

(b) What is the probability that the selected shaft conforms

to surface finish requirements or to roundness require-

ments?

(c) What is the probability that the selected shaft either con-

forms to surface finish requirements or does not conform

to roundness requirements?

(d) What is the probability that the selected shaft conforms to

both surface finish and roundness requirements?

2-54. Cooking oil is produced in two main varieties: mono-

and polyunsaturated. Two common sources of cooking oil are

corn and canola. The following table shows the number of

bottles of these oils at a supermarket:

type of oil

canola corn

type of mono 7 13

unsaturation poly 93 77

(a) If a bottle of oil is selected at random, what is the proba-

bility that it belongs to the polyunsaturated category?

(b) What is the probability that the chosen bottle is monoun-

saturated canola oil?

2-55. A manufacturer of front lights for automobiles tests

lamps under a high humidity, high temperature environment

using intensity and useful life as the responses of interest. The

following table shows the performance of 130 lamps:

useful life

satisfactory unsatisfactory

intensity satisfactory 117 3

unsatisfactory 8 2

(a) Find the probability that a randomly selected lamp will

yield unsatisfactory results under any criteria.

(b) The customers for these lamps demand 95% satisfactory

results. Can the lamp manufacturer meet this demand?

2-56. The shafts in Exercise 2-53 are further classified in terms

of the machine tool that was used for manufacturing the shaft.

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