Let's break this argument down. We know that of 100 people who have not used cocaine, five will test positive when tested. We also know that of 100 people who have used cocaine, 99 will test positive when tested. The conclusion goes on to conclude that when a RANDOM group of people is tested for cocaine use, "the vast majority of those who test positive will be people who have used cocaine."
Now, what's the error in this argument? We do not know what the prevalence of cocaine use is in our population. If a very small proportion of the population uses cocaine, then it is less likely that when a randomly chosen group of people is tested for cocaine use, the vast majority of those who test positive will be those who have used cocaine. It will be more likely, in this case, that the vast majority who test positive will be of the small percentage of non-cocaine users who test positive for it. Thus, an essential piece of the puzzle is missing: what percentage of the population has used cocaine.
(A) is incorrect because the argument does not make a value judgment.
(B) is incorrect because we have no information on the properties of the average member of the population. This is an answer choice for a part-to-whole argument. However, we are not dealing with a part-to-whole flaw in our passage. Thus, this is not the correct answer.
(C) is CORRECT because it clearly outlines the flaw. If there are very few people who have tried cocaine, then when a randomly chosen group of people is tested for cocaine use, the vast majority of those who test positive will not be those who have used cocaine. Rather, it will be those who test positive for cocaine even though they are non-cocaine users. We need to know how prevalent cocaine use is before we can make the conclusion made in the argument.
(D) is incorrect because it is irrelevant. It doesn't affect the argument if some cocaine users do not test positive, and, more so, the stimulus does address this by saying that 99 out of 100 will test positive, meaning one will not test positive. So, in fact, the argument does not ignore this fact.
(E) is incorrect because the stimulus does not advocate this. The stimulus merely argues that due to five positive tests out of every 100 people who have not used cocaine, and 99 positive tests out of every 100 people who have used cocaine, people who test positive from a random sample of people tested for cocaine are those who have used cocaine.
Hope that helps! Let me know if you have any other questions!
RKHanda13November 20, 2013
Therefore, flaw of probabilistic vs. absolute?
MehranNovember 22, 2013
The flaw here is that we have two different possibilities but the author ignores one of them.
The first possibility is that we are testing people who have not used cocaine where 5 out of 100 will test positive. The second possibility is that we are testing people who have used cocaine where 99 out of 100 will test positive.
Then the author takes a randomly chosen group of people tested for cocaine use and concludes from it that the vast majority of those who test positive will be people who have used cocaine. The author is assuming we are in the second possibility (i.e. people who have used cocaine) and completing ignoring the first (i.e. people who have not used cocaine).
To see this more clearly, imagine we chose a randomly selected group of 100 people, none of which had used cocaine. Out of these 100 people, 5 will test positive but none of these 5 have ever used cocaine. As such, the author's conclusion that "the vast majority of those who test positive will be people who have used cocaine" doesn't follow.
We would need to know what proportion of the population have used cocaine to help us determine if we are closer to possibility one or possibility two.
Hope this helps! Please let us know if you have any other questions.
