Greenwood press
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PROBABILITY of binomial situations can be estimated with normal distributions. (See Standard Deviation.) Probability arguments are common in court cases. DNA (deoxyribonucleic acid) matching gives a probability that blood, semen, or hair found at a crime scene matches the accused. The early cases of prosecution based on DNA match- ing produced lengthy arguments about the accuracy of the techniques and the computation of the probabilities. For example, some of the genetic markers that are used in establishing probabilities occur in different proportions in different racial groups. By 1996, recommendations from the National Research Council, the National Institute of Justice, and other government and legal organizations resulted in standardized laboratory techniques and computations of probabilities, so DNA evidence is as well accepted as fingerprint matches. Probabilities have been used to determine whether juries were representative in gender and racial composition to the communities they served. Lawyers for Al Gore and George W. Bush used probability arguments before Florida courts to persuade judges that their respective parties should prevail in the contested pres- idential election of 2000. In the Microsoft antitrust case, the Department of Justice presented probabilities that the Microsoft Corporation would force other companies out of business. Courts have based financial awards to patients whose cancer was misdiagnosed by doctors on computations of the patients’ reduced probability of survival. Probabilities can be computed from geometry formulas. Consider balls falling uniformly on a square piece of cardboard 20 inches on a side that has a circular hole 5 inches in diameter. The proportion of balls that fall through the hole is pro- portional to the ratio of area of hole to area of the cardboard. This would be com- puted using the formulas for area of circle and square: π(2.5) 2 20 2 ≈ 0.049. A ball has about a 5 percent chance of falling through the hole rather than bouncing off the cardboard. Winning carnival games is much more difficult than it appears! online sources for further exploration The geometry junkyard shows geometric probability problems The birthday problem Discrete probability Diffusion Lottery odds calculations Download 1.81 Mb. Do'stlaringiz bilan baham: |
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