#13 - A recent study of 10,000 people who were involved in

[Nikki Siclunov]

There are three things you need to keep in mind: drivers, accidents, and injuries. Think of them as three concentric circles. The author concludes that large car drivers (SUV drivers) have a lower risk of injury than small car drivers (Corolla drivers). There are many ways to calculate this in general (some take the number of miles driven into account, for instance), but for the sake of the argument contained in the stimulus, this is a simple ratio of the number of injuries sustained over the total number of drivers of each car type. This ratio, the author claims, favors SUV drivers. The conclusion is faulty, because it is crucial to know how likely it is that a given Corolla driver gets into an accident vs. a an SUV driver.

The second part of your response makes no sense to me (sorry), and you might want to re-read it carefully. What if, you ask, SUV's have a higher probability of getting into an accident than Corollas? Well, let's say there are 100 SUV drivers, and 100 Corolla drivers. Of them, 50 SUV's get into accidents over their lifetime, but only 10 Corolla's do. According to the results of the study, SUV drivers are less likely to sustain injuries once they get into an accident than Corolla drivers would be. Fine. Let's say only 10 SUV drivers get injured vs. 9 of the 10 Corolla drivers (20% and 90% of those who got in accidents, respectively). The total number of injured Corolla drivers is still lower than the total number of injured SUV drivers (9<10). Since I'm assuming there are 100 drivers of each vehicle, these numbers translate into percentages as well. Clearly, it is possible that SUV drivers are exposed to a higher risk of injury than Corolla drivers.

Your hypothetical assumes an extreme scenario in which SUV drivers have almost no risk of injury. This is untenable, and misleading. Instead of playing around with hypotheticals, you're better off carefully examining the parameters established in the stimulus.

[voodoochild]

Nikki,
Thanks for your reply.

There are three things you need to keep in mind: drivers, accidents, and injuries. Think of them as three concentric circles. The author concludes that large car drivers (SUV drivers) have a lower risk of injury than small car drivers (Corolla drivers). There are many ways to calculate this in general (some take the number of miles driven into account, for instance), but for the sake of the argument contained in the stimulus, this is a simple ratio of the number of injuries sustained over the total number of drivers of each car type. This ratio, the author claims, favors SUV drivers. The conclusion is faulty, because it is crucial to know how likely it is that a given Corolla driver gets into an accident vs. a an SUV driver.

I hate to disagree. The validity of conclusion depends on "how" the likelihood is calculated. That's the main point I am trying to convey. The conclusion doesn't make it clear, at least to me, what parameters are considered while saying the conclusion. In your example, why are you calculating the probability of accidents? We are already given that 10k people met with an accident.

Mathematically speaking, and quoting premise, if 10K people who were involved in an accident, say 10 people of 100 large cars were injured and 100 people of 100 small cars were injured, then probability that someone who has met with an accident and driving a large car will be 0.1. This is a fact. The conclusion also states "in an automobile accident" that means, one wouldn't have to worry about the probability of accidents at all. Had the conclusion been "one is less likely to be injured if one is driving a large car vs. small car..." it would be a completely different story because we would need to calculate the probability of accidents. Hence, I disagree. I still don't know a good way to read the conclusion so that the logic would make sense.

Your hypothetical assumes an extreme scenario in which SUV drivers have almost no risk of injury. This is untenable, and misleading. Instead of playing around with hypotheticals, you're better off carefully examining the parameters established in the stimulus.

Nope. That's not at all correct. I chose probabilities of 10%, 50%,1% and 90%. These probabilities conform to "far more likely", "high" and "low" percentages in the prompt. These are not "extremely unlikely" scenarios. (For convenience, I am presenting the math I did above again. Please correct me if anything is wrong.)

L = probability that a large car is in accident;
S = probability that a small car is in accident.
Dl = low percentage of large car drivers get injured in an accident.
Ds = High percentage of small car drivers get injured in an accident.

Given - D) L> S. Let L= 50% and S = 10%.
Premise => Let Dl = 1% and Ds = 90%

Thus L*Dl = .5 * .01 = .005
S*Ds = .1 * .9 = .09
(to your point about "extremely unlikely" -- we still have leeway to increase L*Dl to be less than .09!)
Thus, D strengthens! The bigger question is that how do we choose whether something strengthens or weakens in less than a minute. We never know what our brain could think on Doom's day.

[Steve Stein]

Let me jump in here--this is an interesting question, and I think it can perhaps be better understood without numbers:

The author's conclusion is that you are more likely to be injured in a small car than in a large car, based on a study that showed a smaller percentage of injuries among large car accident victims. Since the stimulus is followed by a Weaken question, the correct answer choice will be the one that calls into question the author's conclusion.

Correct answer choice D provides this weakener: if large cars are far more likely to be involved in an accident to begin with, then this weakens the general conclusion that you're better off in a larger car--because even if injury is less likely for each accident one has in a large car, this choice provides that large car drivers experience more accidents overall. This weakens the claim that people in big cars are safer overall.

Let me know if that makes sense--this can be a pretty tricky question--thanks!

~Steve

[voodoochild]

Thanks Steve for your response. However, your response ignores the analysis I have written above. I am not sure whether you saw that there are conditions when this argument could be strengthened using D).

Please help me!

Thanks

[Steve Stein]

Thanks Steve for your response. However, your response ignores the analysis I have written above. I am not sure whether you saw that there are conditions when this argument could be strengthened using D).

Please help me!

Thanks

Thanks for your response, but it ignores the analysis that I have written above Since it is much more important that you understand how the correct answer choice weakens the argument, please let me know.

I looked over your numbers, and answer choice D still fails to strengthen the author's argument. I really think it's vital to understand the reasoning:

The author's conclusion is that one is less likely to be injured in a large car than in a small car. One is safer from injury in a large car.

The answer choice that you say strengthens this--is that large cars are more likely to get into an accident.

Please let me know your thoughts--thanks!

~Steve

[Nikki Siclunov]

Mathematically speaking, and quoting premise, if 10K people who were involved in an accident, say 10 people of 100 large cars were injured and 100 people of 100 small cars were injured, then probability that someone who has met with an accident and driving a large car will be 0.1. This is a fact.

No, it isn't. The probability that someone is injured once they get into an accident while driving a large car is 0.1. But if large-car drivers are a lot more accident-prone, the risk that any one such driver is injured in an accident increases. For instance, if the accident rate of large car drivers were 100% and their risk of injury once in an accident were 0.1, then the overall risk of injury to a large driver would be 0.1. By contrast, let's say the probability of someone being injured in an accident while driving a Corolla is 100%. If such drivers almost never get into accidents (say, only 1/1000 Corollas get into accidents), then the overall risk of injury to any one Corolla driver would be much lower (i.e. 0.01).

You fail to distinguish between "risk of injury in an accident" vs. "overall risk of injury to driver." The latter must factor in not only the risk of injury in an accident, but also the risk that an accident will take place:

Overall risk of injury to driver = Risk of injury in an accident (x) Risk of accident

I hope this clears things up.

[persde]

Hello all. I want to make sure I'm thinking about this problem correctly.

The first thing I noticed is that the conclusion contains conditional reasoning: Driving a large car (rather than small car) less likely to be injured in an auto accident. Since this is a "weaken" question, I want to focus on the necessary condition.

Choice (A) has a null effect on the necessary condition; the conditional relationship does not deal with speed.

Choice (B) has a null effect on the necessary condition; the answer does not address accidents or injuries.

Choice (C) has a null effect on the necessary condition; the conditional relationship does not deal with medium- sized cars.

Choice (D) does attack the necessary condition because although the stimulus said that there were fewer injuries for those in large cars, nothing is mentioned about the likelihood of being in an accident for small cars versus large cars. If the likelihood of being in an accident were the same for a small and a large car, the conclusion would make sense. However, if large cars are more accident- prone than small cars, that would call into question the conclusion. It's not a strong attack on the conclusion but it does weaken it to a degree.

Choice (E) has a null effect on the necessary condition; there is no mention of car size related to the accidents or injuries.

Is my thinking correct here?

[Jennifer Janowsky]

Hello all. I want to make sure I'm thinking about this problem correctly.

The first thing I noticed is that the conclusion contains conditional reasoning: Driving a large car (rather than small car) less likely to be injured in an auto accident. Since this is a "weaken" question, I want to focus on the necessary condition.

Choice (A) has a null effect on the necessary condition; the conditional relationship does not deal with speed.

Choice (B) has a null effect on the necessary condition; the answer does not address accidents or injuries.

Choice (C) has a null effect on the necessary condition; the conditional relationship does not deal with medium- sized cars.

Choice (D) does attack the necessary condition because although the stimulus said that there were fewer injuries for those in large cars, nothing is mentioned about the likelihood of being in an accident for small cars versus large cars. If the likelihood of being in an accident were the same for a small and a large car, the conclusion would make sense. However, if large cars are more accident- prone than small cars, that would call into question the conclusion. It's not a strong attack on the conclusion but it does weaken it to a degree.

Choice (E) has a null effect on the necessary condition; there is no mention of car size related to the accidents or injuries.

Is my thinking correct here?

This looks great to me! Good work.

[persde]

Thank you!

[Dianapoo]

Hey Voodoo,

I'm afraid you are over-thinking this problem, and, at the same time, not reading the stimulus carefully enough. I think the latter problem is causing the former, but then again I could be mistaken.

Here's how you should approach this question: the author concludes that large car drivers have a lower risk of injury than small car drivers. This is based on the premise that a relatively low percentage of large car drivers were injured at the time of their accident. This argument omits to take into account a crucial element: how likely is it that a given car (large or small) gets into an accident in the first place? If the likelihood were exactly the same, then the conclusion makes sense: indeed, large car drivers would have a lower risk of injury than small car drivers. Inversely, if large car drivers are generally more accident-prone than small car drivers are, then their overall risk of injury may be higher, even if comparatively fewer of them are injured once the accident occurs.

To put this in numerical terms, the study shows that the following ratio favors large car drivers:

#injuries
-----------
#accidents

The author takes that to mean that the following ratio also favors large car drivers:

#injuries
------------
#drivers

This is clearly a mistake, because the following ratio is unknown for each car type:

#accidents
------------
#drivers

Does this make sense? Let me know.

Hmm I'm not sure I agree with this. I believe you are changing the conclusion without knowing it when you say "large car drivers have a lower risk of injury than small car drivers". The author doesn't seem to be saying this at all! The author is simply referring to the likelihood of being injured IN AN accident. It never mentioned the lower risk overall, which has very big implications and which makes D correct.

I think the Administrator also made this mistake, but who knows, I'm just a student!