Fundamentals of Probability and Statistics for Engineers

2.29 A machine part may be selected from any of three manufacturers with probabilities
The probabilities that it will functionproperly
during a specified period of time are 0.2, 0.3, and 0.4, respectively, for the three
manufacturers. Determine the probability that a randomly chosen machine part
will function properly for the specified time period.

2.30 Consider the possible failure of a transportation system to meet demand during
rush hour.
(a) Determine the probability that the system will fail if theprobabilities shown in
Table 2.3 are known.

(b) If system failure was observed, find the probability that a ‘medium’ demand

level was its cause.

2.31 A cancer diagnostic test is 95% accurate both on those who have cancer and on
those who do not. If 0.005 of the population actually does have cancer, compute
the probability that a particular individual has cancer, given that the test indicates
he or she has cancer.

2.32 A quality control record panel of transistors gives the results shown in Table 2.4
when classified by manufacturer and quality.
Let one transistor be selected at random. What is the probability of it being:
(a) F rom manufacturer A and with acceptable quality?
(b) Acceptable given that it is from manufacturer C?
(c) From manufacturer B given that it is marginal?

2.33 Verify Equation (2.26) for three events.

2.34 In an elementary study of synchronized traffic lights, consider a simple four-light
system. Suppose that each light is red for 30 seconds of a 50-second cycle, and suppose

and

Table 2.3 Probabilities of demand levels and of system

failures for the given demand level, for Problem 2.30

Demand level P(level) P(system failurelevel)

Low 0.6 0

Medium 0.3 0.1

H igh 0.1 0.5

Table 2.4 Quality control results, for Problem 2.32

Manufacturer Quality

Acceptable M arginal U nacceptable Total

A 128 10 2 140

B 97 5 3 105

C 110 5 5 120

34 Fundamentals of Probability and Statistics for Engineers

p 1 ˆ 0 :25,p 2 ˆ 0 :50,andp 3 ˆ 0 :25.

j

P…Sj‡ 1 jSj†ˆ 0 : 15

P…Sj‡ 1 jSj†ˆ 0 : 40