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# When 100 people who have not used cocaine are tested for

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When 100 people who have not used cocaine are tested for [#permalink]  31 Mar 2004, 12:04
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When 100 people who have not used cocaine are tested for cocaine use, on average only 5 will test positive. By contrast. of every 100 people who have used cocaine 99 will test positive. Thus, when a randomly chosen group of people is tested for cocaine use. the vast majority of those who test positive will be people who have used cocaine.

A reasoning error in the argument is that the argument

(A) attempts to infer a value judgment from purely factual premises.

(B) attributes to every member of the population the properties of the average member of the population.

(C) fails to take into account what proportion of the population have used cocaine.

(D) ignores the fact that some cocaine users do not test positive.

(E) advocates testing people for cocaine use when there is no reason to suspect that they have used cocaine.
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[#permalink]  31 Mar 2004, 14:19
I'm with C
D can be refuted because the conclusion says that "the majority of those who test positive will be people who have used cocaine" leaves some leeway that (D) "some cocaine users do not test positive" can still be true. Hence, saying that (D) ignores that some... is wrong.

Category 1: 5% of people who do not use cocaine will test positive for it
Category 2: 99% of people who use cocaine will test positive for it

B is not necessarily the flaw in the reasoning. If we actually take 1 person who tests positive, there is just an equal chance that he will be part of category 1 as category 2. The only way for us to know is to find out what proportion of the whole population belongs to category 1 and what proportion belongs to category 2.

For instance, if there is 1000 people who used cocaine and 99,000 who did not. Then, we know that 1% of the population used cocaine(and it usually is the case that there are less people of a whole population who use drugs than people who do not use it. Otherwise, we would be living in mad city). Also, we will know that .99% of the people who tested positive will actually have used cocaine. Conversely, we will also know that .05*99% = 4.95% of people who tested positive did not use cocaine. Therefore, someone who tested positive has more chance (4.95%) of falling within the people who did NOT use cocaine than falling within the people(.99%) who DID use cocaine. Therefore, the conclusion that "the vast majority of those who test positive will be people who have used cocaine" is totally wrong. C must therefore be the error in the reasoning. Was that right?
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[#permalink]  31 Mar 2004, 17:12
I will go with C on this one.
I haven't read what Paul has written but he sure reduced some load if C is correct.

My simple reasoning is that let us say 5 people are choosen at random who have notused cocaine then they might test +ve. Probability that 5 in 100 will test false +ve does not mean if u choose 5 people at random they will not test false +ve
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[#permalink]  31 Mar 2004, 18:18
vivek_dj wrote:

Vivek.

The director's bias of claiming that the vast majority of those who test positive are indeed those people who have used cocaine is indeed wrong but saying it to be a value judgement is too vague and too weak. You have to be able to directly attack the claim as to how it is wrong as reasoning. Merely saying that it is a value judgement is not as strong as pointing out in C that he fails to consider the different proportions of those using and those not using cocaine.
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[#permalink]  31 Mar 2004, 22:31
Thanks for the explanation Paul...

Vivek.
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[#permalink] 31 Mar 2004, 22:31
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# When 100 people who have not used cocaine are tested for

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