Probability Case Closed
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AP STATISTICS | Case Closed!
False Alarms at Airports False-positives are disruptive. Having one’s luggage flagged as possibly carrying a bomb stigmatizes innocent passengers as potential terrorist suspects. False-positives at the airport lead to embarrassment and humiliation as well as delays. False-positives are costly. Hand-searches of airport luggage mean more wage-earning workers, raising the total cost of airport security from $5 to $7 per passenger. More important, false-positives undermine the effectiveness of hand-searchers. If there are only a few alarms a day, screeners can investigate them thoroughly. If there are dozens, screeners will feel pressured to hurry and may become desensitized to the routine and miss something important. A recent Government Accounting Office report found that the detection of weapons or bombs has not improved much since 2003. In a separate Federal Aviation Administration test of the effectiveness of airport screening systems, 40 percent of explosives, 30 percent of guns, and 70 percent of knives planted by government agents made it through such security checkpoints. Using what you have learnt about simulations and probability, you should now be able to answer some questions about false-positives and false-negatives in connection with the screening of luggage at airports. 1. If a false alarm is a false-positive, what is a false-negative? 2. Which is a more serious error in airport baggage screening, a false-positive or a false-negative? Justify your answer. 3. It is said that the occurrence of false-positives in airport screenings has been about 30%. What does that mean? Write this as a probability statement. 4. Assume that on average 1 suitcase in 10,000 has a bomb in it. Construct a tree diagram to help you find the probability that a suitcase with a bomb would be detected. What is the probability that a piece of luggage that has a bomb in it would escape detention? 5. Find the probability that no alarm is sounded for a suitcase that has no bomb.
AP STATISTICS | Case Closed!
ANSWERS: 1. 2. 3. 4. 5.
False-negative when alarm does not go off for luggage that contains explosives False-negative is much more serious than a false-positive (embarrassment) p = 0.3 P(negative | bomb) = 40% P(positive | bomb) = 1 – 0.4 = 0.6 P(positive | no bomb) = 0.3, P(negative | no bomb) = 0.7
Webheevers.com/forecasting.htm
False Alarms at Airports False-positives are disruptive. Having one’s luggage flagged as possibly carrying a bomb stigmatizes innocent passengers as potential terrorist suspects. False-positives at the airport lead to embarrassment and humiliation as well as delays. False-positives are costly. Hand-searches of airport luggage mean more wage-earning workers, raising the total cost of airport security from $5 to $7 per passenger. More important, false-positives undermine the effectiveness of hand-searchers. If there are only a few alarms a day, screeners can investigate them thoroughly. If there are dozens, screeners will feel pressured to hurry and may become desensitized to the routine and miss something important. A recent Government Accounting Office report found that the detection of weapons or bombs has not improved much since 2003. In a separate Federal Aviation Administration test of the effectiveness of airport screening systems, 40 percent of explosives, 30 percent of guns, and 70 percent of knives planted by government agents made it through such security checkpoints. Using what you have learnt about simulations and probability, you should now be able to answer some questions about false-positives and false-negatives in connection with the screening of luggage at airports. 1. If a false alarm is a false-positive, what is a false-negative? 2. Which is a more serious error in airport baggage screening, a false-positive or a false-negative? Justify your answer. 3. It is said that the occurrence of false-positives in airport screenings has been about 30%. What does that mean? Write this as a probability statement. 4. Assume that on average 1 suitcase in 10,000 has a bomb in it. Construct a tree diagram to help you find the probability that a suitcase with a bomb would be detected. What is the probability that a piece of luggage that has a bomb in it would escape detention? 5. Find the probability that no alarm is sounded for a suitcase that has no bomb.
AP STATISTICS | Case Closed!
ANSWERS: 1. 2. 3. 4. 5.
False-negative when alarm does not go off for luggage that contains explosives False-negative is much more serious than a false-positive (embarrassment) p = 0.3 P(negative | bomb) = 40% P(positive | bomb) = 1 – 0.4 = 0.6 P(positive | no bomb) = 0.3, P(negative | no bomb) = 0.7
Webheevers.com/forecasting.htm
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