Self-study
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. ███ ███████ ████ ███████████ █████ ███ ████████ ███ ████ ███ ███████ ██ ███ ██████ ██ ███████ ████ ███████ ██ ███████████ ████ ██ ███████████ ███ ██ █ ███████ ██████ ██████████ ████ ████████ ██ ████████
Argument Summary
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.
How Common Are Explosives?
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:
100 bags WITH explosive
All caught (100%)
100 real alerts
9,900 bags with NO explosive
1% trigger false alerts
99 false alerts
Total alerts: 199. Real alerts: 100 (about 50%, nowhere near 99%).
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.
Analysis by Kevin_Lin
24.
The reasoning in the argument ██ ██████ ███████ ███ ████████
a
ignores the possibility ██ ███ ███████████ ███████ ██ ██████ ██ █████ ████ ███ ███████ ████ ███████ ██ █████████
b
draws a general ██████████ █████ ███████████ ██ ███ █████ ██ █ ██████ ████ ██ ██████ ██ ██ ██████
c
ignores the possibility ██ █████ █████ ██ ███ ████ ██ ███ ███████████ ████████ ████ ███ ███████ ███ ███████ ███ ██ ███
d
fails to acknowledge ███ ███████████ ████ ███ ███████ ████ ███ ██ ███████ █████████ ██ ███ █████ ██ ██████████
e
substitutes one group ███ █ █████████ █████ ██ ███ █████████ ██ █ ██████████