Support A certain airport security scanner designed to detect explosives in luggage will alert the scanner’s operator whenever the piece of luggage passing under the scanner contains an explosive. ███ ███████ ████ ███████████ █████ ███ ████████ ███ ████ ███ ███████ ██ ███ ██████ ██ ███████ ████ ███████ ██ ███████████ ████ ██ ███████████ ███ ██ █ ███████ ██████ ██████████ ████ ████████ ██ ████████
The scanner has two stated capabilities. First, it catches every bag that contains an explosive. Second, it falsely alerts on just 1% of bags that don't contain explosives (a low false positive rate).
From these two facts, the argument concludes that 99 out of 100 alerts are for actual explosives. That's a leap.
The argument's reasoning seems to be: if only 1% of clean bags trigger a false alert, then 99% of alerts must be true alerts of bags with explosives. The math feels intuitive, but it skips a crucial question: how common are explosives in luggage to begin with?
That number is the missing piece. If most bags don't have explosives (which is almost certainly true), then a 1% false-alert rate, applied to a giant pool of clean bags, can easily produce more alerts than the bags with actual explosives do.
Suppose 10,000 bags pass through the scanner and 1 in 100 contains an explosive:
And if explosives are rarer than 1 in 100 (which they certainly are in real life), the share of real alerts drops further still. Without knowing how common explosives are across all bags, we can't conclude anything about what fraction of alerts are genuinely catching explosives.
The reasoning in the argument ██ ██████ ███████ ███ ████████
ignores the possibility ██ ███ ███████████ ███████ ██ ██████ ██ █████ ████ ███ ███████ ████ ███████ ██ █████████
The stimulus actually addresses this. We're told in the first sentence, which is a premise, that the scanner alerts whenever a bag contains an explosive. So missed detections aren't possible.
draws a general ██████████ █████ ███████████ ██ ███ █████ ██ █ ██████ ████ ██ ██████ ██ ██ ██████
The argument doesn't rely on a sample. It states the scanner's reliability rates as given facts about the device, not as estimates from sampling. So sample bias isn't the issue.
ignores the possibility ██ █████ █████ ██ ███ ████ ██ ███ ███████████ ████████ ████ ███ ███████ ███ ███████ ███ ██ ███
What the operator does after the alert doesn't change how many of the alerts are real to begin with. The conclusion is about the percentage of alerts that actually contain explosives, not about whether the operator will recognize the alerts or take appropriate action.
fails to acknowledge ███ ███████████ ████ ███ ███████ ████ ███ ██ ███████ █████████ ██ ███ █████ ██ ██████████
Different levels of sensitivity to different explosives won't affect the argument, because we already have a premise establishing that whenever luggage passing under the scanner has an explosive, the scanner will alert. So, 100% of the time, no matter the kind of explosive, if it passes under the scanner, there will be an alert.
substitutes one group ███ █ █████████ █████ ██ ███ █████████ ██ █ ██████████
This probably isn't worded in a way that you'd expect, but it can describe what the argument does. The 1% rate mentioned in the second sentence is a percentage of bags without explosives. Only 1% of bags without explosives will set off an alert. But the author interprets that claim as though it means only 1% of alerts involve a bag without explosives. The author substitutes one group (instances when an alert occurs) with another group (instances involving a bag without an explosive).
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