# computer networking Exercises Chapter 5 Exercises 1, 2, 3, 4, 6, 8, 11, 12. indi Ing judgments about probabilities. Often the receipt of new infor mation,

computer networking Exercises Chapter 5 Exercises 1, 2, 3, 4, 6, 8, 11, 12. indi

Ing judgments about probabilities. Often the receipt of new infor

mation, such as market research results or provisional sales figures, can be used to

modify initial probability assessments, and in Chapter 9 we will show how this revi-

sion of opinion should be carried out.

Above all, the correct application of the rules and concepts which we have intro-

duced in this chapter requires both practice and clarity of thought. You are therefore

urged to attempt the following exercises before reading further.

Exercises

Additional exercises can be found on the book’s website.

(1) Determine the probability of each of the following events occurring. State the

approach to probability which you used and any assumptions which you

needed to make.

113

EXERCISES

are

(a) A person selected from the payroll of a company is a clerical worker given

that there are 350 people on the payroll of whom 120 are clerical workers.

(b) A light bulb selected from a production line is defective if, out of 400 bulbs

already tested, eight were defective.

400

(c) A newborn baby is male,

(d) This month’s sales forecast for a product has an error of more than 10% if

the forecast had an error of over 10% in 21 out of the last 60 months.

(e) A permanently manned space station is established on Mars by the year

(2) The following table shows an estimated probability distribution for the sales of

a new product in its first week:

2050.

Number of units sold

o

1

2

3

4

5

Probability

0.05

0.15 0.20 0.35

0.15 0.10

What is the probability that in the first week:

(a) 4 or 5 units will be sold?

(b) At least 3 units will be sold?

(c) At least 1 unit will be sold?

(3) The managers of a food company are interested in determining the effect on their

sales of a competitor’s television advertisements. An analysis of sales records for

the last 120 weeks gives the following results:

Level of sales

Total no.

of weeks

Low

Medium

High

Competitor advertised

Competitor did not advertise

Total

32.

21

153

14

12

26

18

23

41

64

56

120

Assuming that these past data are a reliable guide to the future, determine the

probability that next week:

(a) The competitor will advertise.

(b) Sales will not be high.

(c) Medium or high sales will be achieved.

CISES

INTRODUCTION TO PROBABILITY

114

(a) Assuming

probabilities:

(d) Either the competitor will advertise or only low sales will be achieved.

(e) Either the competitor will not advertise or high sales will be achieved

(4) (a) With reference to the table in question 3, determine the following

(ii) p(next week’s sales will be high the competitor advertises)

(iii) p(next week’s sales will be high the competitor does not advertise)

(iv) p(next week’s sales will be low)

(v) p(next week’s sales will be low the competitor advertises).

(b) Do the events ‘competitor advertises’ and ‘high sales’ appear to be indepen-

dent?

(5) Given below are the results of a survey of 100 cars:

mine the

of the wee

(b) Do you th

individus

The manage

they are cur

that there is

the product

probability

that the m

high?

) An engine

trophe oc

a malfun

Condition of brakes

Faulty Not faulty

Total

Condition of tires

Faulty

Not faulty

Total

25

15

40

5

55

60

30

70

100

the prob

0.001 pro

safety d

What is

the ove

110) The pr

week

shares

the pe

is the

(a) Assuming that the survey is representative of all the cars on the road, v

is the probability that a car selected at random will have:

(i) Faulty brakes?

(ii) Faulty tires?

(iii) Either faulty brakes or faulty tires?

(iv) Faulty brakes given that it has faulty tires?

(v) Faulty tires given that it has faulty brakes?

(b) What conclusion would you draw about the relationship between the events

“faulty tires’ and ‘faulty brakes’?

(6) Three machines A, B and C operate independently in a factory. Machine A is

out of action for 10% of the time, while machine B is out of action for 5% of the

time and machine C for 20% of the time. A rush order has to be commenced at

midday tomorrow. What is the probability that at this time:

(a) All three machines will be out of action?

(b) None of the machines will be out of action?

(7) A speculator purchases three stocks on the London Stock Exchange. He esti-

mates that the probabilities that each of these stocks will have risen in value by

the end of the week are, respectively, 0.6, 0.8 and 0.4.

O PRON

EXERCISES

115

hieved

e follow

of the week.

Avertise

e indepe

high?

(a) Assuming that the price changes in the three stocks are independent, deter-

mine the probability that all three stocks will have risen in value by the end

(b) Do you think that it is reasonable

to assume that movements in the prices of

individual stocks are independent?

(8) The managers of a company are considering the launch of a new product and

they are currently awaiting the results of a market research study. It is thought

that there is a 0.6 probability that the market research will indicate that sales of

the product in its first 3 years will be high. If this indication is received then the

probability that sales will be high is thought to be 0.8. What is the probability

that the market research will indicate high sales and sales will turn out to be

(9) An engineer at a chemical plant wishes to assess the probability of a major catas-

trophe occurring at the plant during the overhaul of a processor as a result of

a malfunction in the equipment being used in the overhaul. He estimates that

the probability of a malfunction occurring is 0.1. If this happens there is only a

0.001 probability that a safety device will fail to switch off the equipment. If the

safety device fails, the probability of a major catastrophe is estimated to be 0.8.

What is the probability that a major catastrophe will occur at the plant during

the overhaul as a result of the equipment malfunctioning?

(10) The probability of the Dow

Jones index rising on the first day of trading next

week is thought to be 0.6. If it does rise then the probability that the value of

shares in a publishing company will rise is 0.8. If the index does not rise then

the publishing company’s shares will only have a 0.3 probability of rising. What

is the probability that the publishing company’s shares will rise in value on the

first day of trading next week?

(11) A car owners’ club which offers a rescue service for stranded motorists has to

make a decision on the number of breakdown patrols to deploy between mid-

night and 8 a.m. on weekdays during the summer. The number of requests for

assistance received by a local office during these hours follows the probability

distribution shown below.

1. what

Vents

Ais

f the

ed at

1

2

3

4

5

No. of requests received 0

Probability

0.01 0.12 0.25 0.42 0.12 0.08

sti

by

(a) Calculate the expected number of requests received and interpret your

results.

(b) Is this a discrete or a continuous probability distribution?

INTRODUCTION TO PROBABILITY

116

(12) You are thinking of selling your house and you reckon that there is a

0.1 probability that you will sell it for $120 000, a 0.5 probability that you

will receive $100 000 for it and a 0.4 probability that you will only receive

$80 000. What is the expected selling price of the property? Interpret your

result.

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