Out of 100 people who don’t do cocaine: 5 test positive on average.
We can say 5% of (ppl who do NOT do cocaine test positive)
Out of 100 people who DO cocaine: 99 test positive on average
We can say that 99% of (ppl who DO cocaine will test positive)
Conclusion: the vast majority of those who TEST POSITIVE (from a randomly selected group) will be those who DO cocaine
This is similar to a weighted average set up in the quant section (something that the GMAT apparently loves to play around with).
Out of the entire population from which we are picking these random people, we do not know the “relative weighting” of the people who DO cocaine vs. the people who do NOT do cocaine.
For example, say we have 100 people in a hypothetical world.
99 do NOT do cocaine. Only 1 person does cocaine.
5% (99) = test positive but did NOT do cocaine
99% (1) = test positive and DID do cocaine
5% of 99 ~ 5 people tested positive who did NOT do cocaine
99% of 1 ~ 1 person who tested positive and actually DID the cocaine
Out of these 6 people who tested positive, the vast majority is those people who did NOT do cocaine (5 out of 6)
Because we do not know what proportion of the population actually does cocaine, we can’t make the conclusion that OUT OF those who TEST POSITIVE, most will have actually done cocaine
C
neelabhmahesh wrote:
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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