Q24 - A certain airport security

[skapur777]

Is A incorrect because the author DOES mention the possibility of the scanner failing to signal a luggage with explosives, but does so erroneously?

But what exactly is E saying? I understand how B, C, and D are incorrect.

But how is one group being substituted for another here "in the statement of a percentage"?

[bbirdwell]

Anytime you see statistics on the LSAT, you need to take a close look at which groups are being discussed.

Here, we have "luggage" in general, and "luggage that contains no explosives."

Please consider that distinction and see if you still have questions.

[skapur777]

Ohh, I think I see. He says that it will alert only one percent of luggages that contain no explosives. So 1 in every 100 pieces of luggages that contain no explosives will erroneously ring. But it does not follow that the other 99 are luggages with explosives at all...

[griffin.811]

This was a little tricky for, but I think I have it down now. The premise in our core essentially says that for every 100 pieces of clean luggage we send through the scanner, we will get 1 erroneous alert. (the scanner will alert us that there is an explosive, when in reality there isn't one).

The author then decides from this that 99/100 alerts will be for pieces of luggage that actually do have explosives.

Still don't see it...neither did I...until I thought about it this way:

Let's say I send 10,000 pieces of "clean" luggage through the scanner. I will get 100 erroneous alerts (understand this part before reading further). Now ask yourself will 99 of those alerts be for pieces of luggage that actually have explosives? Nope. Actually none of them will since all the luggage is "clean."

Since we have just dispproved our author's theory, he cannot CORRECTLY, from a LOGICAL stand, draw this conclusion.

Oh, and answer choice (E) states this.

[bbirdwell]

Sounds good to me. Though not essential for the LSAT, at times a little math can help!

[raymondcezar]

This question threw me off a bit, but then I parsed through the stimulus and saw the inconsistency with the core.

The author is actually switching 99% of luggage that contain NO explosives (in the premise) in place for 99% of luggage that do contain explosives (in the conclusion).

E matches up with this flaw.

[seychelles1718]

I know why E is the correct answer but I don't understand why A is wrong. I just think we can't really infer anything about the possibility of scanner's failure to signal an alert when the luggage does contain an explosive....

can anyone explain why A is wrong? Thanks!!!

[ohthatpatrick]

Let me put up a complete explanation since we don't have one here yet.

Question type: Flaw

ARGUMENT CORE

evidence -
There's a new scanner for finding bombs in luggage.
If luggage contains an explosive, then scanner will alert.
If luggage doesn't contain an explosive, scanner will only alert 1 out of 100 times.

conclusion -
Out of every 100 alerts, 99 will be real and 1 will be fake.

ANALYSIS

This is very math-y, so let's think about how he got the math wrong.
We know that this scanner is 100% when it comes to detecting actual bombs.
100 times that there's a bomb, 100 alerts.

We know this scanner is 99% accurate when it comes to detecting safe luggage.
100 scans of safe luggage, only 1 alert.

So what's wrong with saying, "out of every 100 alerts, 99 will be real and 1 will be fake".

Well let's say that the first 100 scans of the day are all safe luggage. (I certainly HOPE that's true at the average airport).

We know that we will have gotten 1 alert.

What if the next 100 scans are also clean?

Now we will have scanned 200 bags, and heard 2 alerts (both false alarms).

You could keep scaling this up ... say that we've done 1000 scans of safe bags -- we will have heard 10 alerts. Once we've scanned 10,000 safe bags, we will have heard 100 alerts. Is it true that 99 of those alerts were genuine bombs?

Of course not. There have been no genuine bombs in this hypothetical. We've just scanned 10,000 safe bags.

ANSWER CHOICES

(A) The author doesn't ignore this possibility. He tells us that the scanner ALWAYS signals an alert when the luggage has an explosive. "A certain scanner ... will alert ... whenever the piece of luggage ... contains an explosive"

(B) He does draw a general conclusion, because he extrapolates a rate for all alerts. But there's no reason to think the sample data is biased. In fact, it's a big stretch to even call the evidence "a sample". We're being given actual rates for a machine. "A sample" refers to some subset of a population. This hardly qualifies. Either way, no evidence it's likely to be biased.

(C) The conclusion is only about assessing the quantity of alerts that occur. It is true or false based on the number of alerts / explosives that occurred or were present. The human response (or lack thereof) to these alerts has nothing to do with the truth value of the conclusion.

(D) Would it hurt the argument if the scanner were not equally sensitive to all types of explosives? If that affected whether or not the scanner would sound an alert, then it would be relevant to our conclusion about "the number of alerts / explosives present". But we already have language in the evidence that says "WHENEVER the luggage contains an explosive, an alert will sound". So differing degrees of sensitivity wouldn't matter, because apparently even the weaker sensitivity is still enough to ALWAYS trigger a warning when the explosive is present.

(E) Not sure at first glance how this expresses the flaw, but it at least relates to the math problem.

The author's conclusion is saying this:
100 alerts = 99 bombs and 1 safe

He thinks that 1 out of every 100 alerts is a false alarm (safe bag).

So he thinks his 2nd sentence really means "For all bags we scan, the scanner will erroneously alert the operator only 1% of the time".

In reality the 2nd sentence says, "For all safe-bags we scan, the scanner will erroneously alert the operator only 1% of the time."

[jiangziou]

I try to use a math equation to explain this flaw.

Pt 5- S1-Q11 is the same flaw type as this one: 5% non-cocaine users will test positive, and 99% cocaine users will test positive, so the vast majority of people who test positive have used cocaine.

For both questions, if we want to know the accuracy of the cocaine test or the security alert , we need the real proportion of the target (cocaine user/explosive luggage) in the total population.



In this question, for explosive luggage the alert rate is 100%, for safe luggage the alert rate is 1%. (a=100%, b=1%)
If we know that there are x explosive luggage in 100 luggage.
Then we can sayalert explosives will actually be present.

Could someone please examine the equation?

[JeremyK460]

thought i'd share another way i came to understanding the flaw in the stimulus!

there's a glaring and tedious math issue that happens between the premise and conclusion, but there's also a categorical issue:

premise: about alerts for luggage WITHOUT bombs (categorically 'negative')
conclusion: about alerts for luggage WITH bombs (categorically 'affirmative')

answer choice: "substitutes one group for a different group in the statement of a percentage"

the 'percentage' part is just an appendage of the flaw itself; it's expendable. i can replace it. for example...

My coin-finder metal detector has erroneously alerted me only once when there was no coin present. Therefore my coin-finder metal detector is almost always right when it alerts me that there is a coin present.

substitutes one group (when there's coin/metal) for a different group (when there is no coin/metal present) in the statement of a percentage

i can't argue for a belief about stuff that happens when coin/metal is present from premises about stuff that happens when coin/metal is not present.

for sure some 'categorical flaw' term for this exists - i just forgot! but a quick google search should find it