lecturemanialecturemania.com/arkakapi/cache/ilbfildersnotu46.pdf · 2009. 9. 30. · lecturemania...

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2.11 Of 25 microcomputers available in a supply room, 10 have circuit boards for a printer, 5 havecircuit boards for a modem, and 13 have neither type of board. Using P to denote those thathave printer boards and M to denote those that have modem boards, symbolically denote thefollowing sets, and give the number of microcomputers in each set.o Those that have both boards.b Those that have neither board.c Those that have printer boards only.d Those that have exactly one of the boards.

2.12 Construct a table to display the data in Exercise 2.11.

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2.13 Five applicants (Jim, Don, Mary, Sue, and Nancy) are available for two identical jobs. Asupervisor selects two applicants to fill these jobs.i List all possible ways in which the jobs can be filled. (That is, list all possible selections

of two applicants from the five.)b Let A denote the set of selections containing ai least one male, How many elements are

in A?( Let B denote the set of selections containing exactly one male, How many elements are

inB?d Write the set containing two females in terms of A and B.e LisUh^elements in A, AB, A U B, and AB.

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\2.1 n A manufacturing company has two retail outlets. It is known that 30% of the potential customers) buy products from outlet I alone, 50% buy from outlet II alone. 10% buy from both I and H, and

10% buy from neither. Let A denote the event that a potential customer, randomly chosen, buysfrom I and B denote the event that the customer buys from II. Find the following probabilities.

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iecturemaniaAmong five portable generators produced by an assembly line in one day, there are two defec-tives. If two generators are selected for sale, find the probability that both will be nondefective.(Assume the two selected for sale are chosen so that every possible sample of size two has thesame probability of being selected.)

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For a certain style of new automobile, the colors blue, white, black, and green are in equaldemand. Three successive orders are placed for automobiles of this style. Find the probabilitythat

a one blue, one white, and one green are ordered.b two blues are ordered.C at least one black is ordered.

d exactly two of the orders are for the same color.

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Nine impact wrenches are to be divided evenly among three assembly lines.0 In how many ways can this be done?

fa Two of the wrenches are used, and seven are new. What is the probability that a particularline (line A) gets both used wrenches?

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$An incoming lot of silicon wafers is to be inspected for defectives by an engineer in a microchipmanufacturing plant. In a tray containing 20 wafers, assume four are defective. Two wafers areto be randomly selected for inspection. Find the probability that

a both are nondefective.

b at least one of the two is nondefective.

t both are nondefective given that at least one is nondefective.

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2.44 Consider the following segment of an electric circuit with three relays. Current will flow froma to b if there is at least one closed path when the relays are switched to "closed." However,the relays may malfunction. Suppose they close properly only with probability 0.9 when theswitch is thrown, and suppose they operate independently of one another. Let A denote theevent that current will flow from a to b when the relays are switched to "closed."

b Find the probability that relay 1 is closed properly, given that current is known to beflowing from a to b.

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A diagnostic test for a certain disease is said to be 90% accurate in that, if a person hasthe disease, the test will detect it with probability 0.9. Also, if a person does not have thedisease, the test will report that he or she doesn't have it with probability 0.9. Only 1% of thepopulation has the disease in question. If a person is chosen at random from the populationand the diagnostic test reports him to have the disease, what is the conditional probability thathe does, in fact, have the disease? Are you surprised by the size of the answer? Would you callthis diagnostic test reliable?

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