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PT32.S1.Q17 - A possible explanation for answer choice C
dcdcdcdcdc
Alum Member
See here: https://7sage.com/lesson/the-embezzler-weaken-question
The Embezzler (weaken EXCEPT question)
This question gave a lot of people trouble, particularly regarding why answer choice (C) weakened the argument. After reflection, I believe I may have unpacked the reason why this is a clear cut wrong answer choice. However, I am wondering how C does not straight up contradict the conclusion of the argument, which we are not supposed to do in weaken questions. I am grateful for any input or feedback on this attempt. Let's begin!
minor premise: embezzler had special knowledge and access
sub-conclusion/major premise 1: embezzler is an accountant or actuary
major premise 2: an accountant would probably not make the mistake which revealed the embezzlement
main conclusion: it is likely that the embezzler is an actuary
Answer choice (C) states that there are 8 accountants and 2 actuaries
This is where things got dicey. Many people felt that the premise that "an accountant would probably not make the mistake" affected the probability that answer choice (C) was hinting at. However,there seem to be two major assumptions made to jump from the premise that "an accountant probably would not make the mistake" to the conclusion that "it is likely an actuary is the embezzler." First, the assumption that, because an accountant probably would not make the mistake, that therefore an actuary probably would make the mistake. Second, and this is a huge unstated assumption, the person who made the mistake is the person who committed the crime.
For example, even if we accept that an actuary has a greater likelihood of making the mistake that led to the discovery of the crime, is it not possible that an actuary could make the mistake but not have committed the crime? Therefore, the likelihood of committing the mistake and the likelihood of committing the crime are separate and distinct from each other. Conflating the two is a major assumption of the argument and a major reason for confusion on answer choice (C).
If we separate the assumption that the person who committed the mistake is the person that committed the crime from the conclusion that an actuary likely committed the crime we can use simple probability in looking at answer choice (C). Granted, this requires us to assume that of all accountant and actuary employees at XYZ Corporation, each person had an equal chance of either committing or not committing the crime. However, this lets us avoid introducing confusion of who was more likely to have committed the crime versus who was more likely to have made the mistake that led to the discover of the crime. Then the answer choice weakens the argument by stating that we would have to concede it seems there is greater probability that an accountant was the person who committed the crime.
That solves it for me.
However, I would really appreciate insight on how this answer choice does not both (1) directly contradict the conclusion and (2) avoids the assumptions that provide the support from premise to conclusion.
Regarding (1), C in English becomes It is likely that an accountant is the embezzler; this is in direct contradiction to the stated conclusion in the stimulus that "it is likely an actuary is the embezzler." Maybe it depends on the definition of "likely?" In other sources, I see it means, possible to be true, but I also see at as being used as probable (that is, in probability we could not say that it is probable if there was actually only a 20% chance, as is the case of actuaries being the culprit in answer choice (C)).
We accept the premises and conclusion as true, as we must for weaken questions. Now if I told you that there is an 80% probability of an accountant being the embezzler, how could you seriously hold on to the truth of your conclusion that "it is likely an actuary is the embezzler?" Unless likely is meant as "could be true?"
Regarding (2), the support provided by the major premise that an accountant would probably not make the mistake ties into the conclusion by (a) assuming the person who commits the mistake also committed the crime and (b) that the actuary is more likely to commit the mistake. Answer choice (C) doesn't go after any of these. It instead focuses on the probability of the person who committed the crime, which seems just attacks the conclusion directly and changes it's outcome.
In other words, looking at the unstated assumption which conflates those who made the mistake with those who committed the crime, the main conclusion really just states a probability that has no relation to the rest of the argument except via extreme assumptions. Then answer choice C directly changes this probability.
After further parsing this, I would actually say the major conclusion does not follow from the premises and that the argument has made the flaw of confusing likelihood of committing the crime with likelihood of making the mistake. The detective spent all his time discussing the likelihood of the mistake but then expressed his conclusion as one of likelihood of committing the crime (which we know nothing about). C introduces information about the likelihood of the occupation for those who could have committed the crime. But this entirely shifts the detective's erroneous conclusion.
Thanks!
The Embezzler (weaken EXCEPT question)
This question gave a lot of people trouble, particularly regarding why answer choice (C) weakened the argument. After reflection, I believe I may have unpacked the reason why this is a clear cut wrong answer choice. However, I am wondering how C does not straight up contradict the conclusion of the argument, which we are not supposed to do in weaken questions. I am grateful for any input or feedback on this attempt. Let's begin!
minor premise: embezzler had special knowledge and access
sub-conclusion/major premise 1: embezzler is an accountant or actuary
major premise 2: an accountant would probably not make the mistake which revealed the embezzlement
main conclusion: it is likely that the embezzler is an actuary
Answer choice (C) states that there are 8 accountants and 2 actuaries
This is where things got dicey. Many people felt that the premise that "an accountant would probably not make the mistake" affected the probability that answer choice (C) was hinting at. However,there seem to be two major assumptions made to jump from the premise that "an accountant probably would not make the mistake" to the conclusion that "it is likely an actuary is the embezzler." First, the assumption that, because an accountant probably would not make the mistake, that therefore an actuary probably would make the mistake. Second, and this is a huge unstated assumption, the person who made the mistake is the person who committed the crime.
For example, even if we accept that an actuary has a greater likelihood of making the mistake that led to the discovery of the crime, is it not possible that an actuary could make the mistake but not have committed the crime? Therefore, the likelihood of committing the mistake and the likelihood of committing the crime are separate and distinct from each other. Conflating the two is a major assumption of the argument and a major reason for confusion on answer choice (C).
If we separate the assumption that the person who committed the mistake is the person that committed the crime from the conclusion that an actuary likely committed the crime we can use simple probability in looking at answer choice (C). Granted, this requires us to assume that of all accountant and actuary employees at XYZ Corporation, each person had an equal chance of either committing or not committing the crime. However, this lets us avoid introducing confusion of who was more likely to have committed the crime versus who was more likely to have made the mistake that led to the discover of the crime. Then the answer choice weakens the argument by stating that we would have to concede it seems there is greater probability that an accountant was the person who committed the crime.
That solves it for me.
However, I would really appreciate insight on how this answer choice does not both (1) directly contradict the conclusion and (2) avoids the assumptions that provide the support from premise to conclusion.
Regarding (1), C in English becomes It is likely that an accountant is the embezzler; this is in direct contradiction to the stated conclusion in the stimulus that "it is likely an actuary is the embezzler." Maybe it depends on the definition of "likely?" In other sources, I see it means, possible to be true, but I also see at as being used as probable (that is, in probability we could not say that it is probable if there was actually only a 20% chance, as is the case of actuaries being the culprit in answer choice (C)).
We accept the premises and conclusion as true, as we must for weaken questions. Now if I told you that there is an 80% probability of an accountant being the embezzler, how could you seriously hold on to the truth of your conclusion that "it is likely an actuary is the embezzler?" Unless likely is meant as "could be true?"
Regarding (2), the support provided by the major premise that an accountant would probably not make the mistake ties into the conclusion by (a) assuming the person who commits the mistake also committed the crime and (b) that the actuary is more likely to commit the mistake. Answer choice (C) doesn't go after any of these. It instead focuses on the probability of the person who committed the crime, which seems just attacks the conclusion directly and changes it's outcome.
In other words, looking at the unstated assumption which conflates those who made the mistake with those who committed the crime, the main conclusion really just states a probability that has no relation to the rest of the argument except via extreme assumptions. Then answer choice C directly changes this probability.
After further parsing this, I would actually say the major conclusion does not follow from the premises and that the argument has made the flaw of confusing likelihood of committing the crime with likelihood of making the mistake. The detective spent all his time discussing the likelihood of the mistake but then expressed his conclusion as one of likelihood of committing the crime (which we know nothing about). C introduces information about the likelihood of the occupation for those who could have committed the crime. But this entirely shifts the detective's erroneous conclusion.
Thanks!
Comments
I'm not sure that the assumption you bring up about the mistake that led to the discovery of the crime vs. the person who committed the crime is terribly important for answer choice (C). Suppose we know the person who committed the crime is different from the person who made the mistake. Suppose, also, we know that there are 900 accountants and 1 actuary. Doesn't this 900:1 ratio still give you reason to think that it's not more likely for an actuary to be the criminal?
I would strongly agree with you that the differentiation isn't really important for C; rather I would state that (at least for myself) separating the probability applied in C and the likelihood discussed in one of the premises was crucial in helping to see C as correct.
I see now that C does not have to contradict the premise as more information about the probability of one or other group committing the crime could result in the conclusion following from the argument. Thanks.