mcm试题04-08资源-CSDN文库

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2004 MCM A: Are Fingerprints Unique?

It is a commonplace belief that the thumbprint of every human who has ever lived is

different. Develop and analyze a model that will allow you to assess the probability

that this is true. Compare the odds (that you found in this problem) of

misidentification by fingerprint evidence against the odds of misidentification by

DNA evidence.

2004 MCM B: A Faster Quick Pass System

“Quick Pass” systems are increasingly appearing to reduce people's time waiting in

line, whether it is at tollbooths, amusement parks, or elsewhere. Consider the design

of a Quick Pass system for an amusement park. The amusement park has

experimented by offering Quick Passes for several popular rides as a test. The idea is

that for certain popular rides you can go to a kiosk near that ride and insert your daily

park entrance ticket, and out will come a slip that states that you can return to that ride

at a specific time later. For example, you insert your daily park entrance ticket at 1:15

pm, and the Quick Pass states that you can come back between 3:30 and 4:30 pm

when you can use your slip to enter a second, and presumably much shorter, line that

will get you to the ride faster. To prevent people from obtaining Quick Passes for

several rides at once, the Quick Pass machines allow you to have only one active

Quick Pass at a time. You have been hired as one of several competing consultants to

improve the operation of Quick Pass. Customers have been complaining about some

anomalies in the test system. For example, customers observed that in one instance

Quick Passes were being offered for a return time as long as 4 hours later. A short

time later on the same ride, the Quick Passes were given for times only an hour or so

later. In some instances, the lines for people with Quick passes are nearly as long and

slow as the regular lines.

The problem then is to propose and test schemes for issuing Quick Passes in order to

increase people's enjoyment of the amusement park. Part of the problem is to

determine what criteria to use in evaluating alternative schemes. Include in your

report a non-technical summary for amusement park executives who must choose

between alternatives from competing consultants.

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