PT13.S2.Q24 - I don't understand this bomb question.

Ashley2018-1

I think I understand what the premises are saying, but I don't understand where the author of this stimulus even got his conclusion. If we have luggages that don't contain explosives and only one percent give false positives (alarm goes off even though there aren't any actual bombs), then how can we conclude that 99/100 alerts=actual bomb threats? Shouldn't the proper conclusion be that there aren't any actual bomb threats in this scenario even if the alarm does go off because the luggages don't have bombs in them? I've always felt there was something wrong with the conclusion, but I just cannot put my finger on what is the actual problem and the abstract nature of E isn't helping.

Edit: Is the conclusion wrong because we don't actually know the proportion of hypothetical luggages that do contain bombs? For example, if we have 1000 luggages and none have bombs, then the conclusion would make no sense since there would be 10 false positives where the alarm goes off, but literally 0 have bombs instead of the 99% accuracy the conclusion is suggesting. I still don't understand which group is being substituted for which though.

Jordan Johnson

@Ashley2018 We can't conclude that 99/100 are actual bomb threats -- that's the flaw in the argument.

The correct answer, E, points to that exact thing -- it tells us that the scanner will erroneously trigger 1% of the pieces of luggage WITHOUT a bomb in them, but we don't know anything about its accuracy for pieces of luggage that DO have a bomb in them. They are two separate groups.

Hope that helps!

Ashley2018-1

@"Jordan Johnson" said:
@Ashley2018 We can't conclude that 99/100 are actual bomb threats -- that's the flaw in the argument.

The correct answer, E, points to that exact thing -- it tells us that the scanner will erroneously trigger 1% of the pieces of luggage WITHOUT a bomb in them, but we don't know anything about its accuracy for pieces of luggage that DO have a bomb in them. They are two separate groups.

Hope that helps!

Is there a situation in which the conclusion would be accurate? It's just so counterintuitive to me to think of luggages that actually do have bombs in them when the premises didn't make any mention of them.

If there were 99/100 luggages that did have bombs, then the conclusion would be true, wouldn't it?

...yeah, I'm gonna need a full stimulus breakdown because there is obviously something big I'm missing.

Jordan Johnson

@Ashley2018 There are two separate populations:
- Luggage that HAS a bomb inside
- Luggage that DOES NOT have a bomb inside

We're only given information on the scanner's performance related to the latter category. 1% of "luggage that DOES NOT have a bomb" accidentally triggers the scanner. That means that 99% of "luggage that DOES NOT have a bomb" doesn't trigger the scanner erroneously.

Without information on the former category, there is no way to deduce the likelihood that the scanner will trigger when the luggage HAS a bomb inside. We would have to be told some statistical information about the number of times the scanner guesses correctly, or the number of times it guesses incorrectly, compared to the entirety of this separate subset.

The only way to reach the specific conclusion in this Flawed Argument is to be given an additional Premise about "Luggage that HAS a bomb inside" -- either that it correctly identifies it 99% of the time, or that it incorrectly identifies it 1% of the time.

Hope that helps!