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A recent survey of all auto accident victims in Dole County

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A recent survey of all auto accident victims in Dole County [#permalink] New post 12 Jul 2008, 04:59
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A recent survey of all auto accident victims in Dole County found that, of the severely injured drivers and front-seat passengers, 80 percent were not wearing seat belts at the time of their accidents. This indicates that, by wearing seat belts, drivers and front-seat passengers can greatly reduce their risk of being severely injured if they are in an auto accident.

The conclusion above is not properly drawn unless which of the following is true?

(A) Of all the drivers and front-seat passengers in the survey, more than 20 percent were wearing seat belts at the time of their accidents.
(B)Considerably more than 20 percent of drivers and front-seat passengers in Dole County always wear seat belts when traveling by car.
(C) More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured.
(D) More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.
(E) Most of the auto accidents reported to police in Dole County do not involve any serious injury.
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Re: CR-Auto accidents [#permalink] New post 12 Jul 2008, 06:03
The conclusion above is not properly drawn unless which of the following is true?

This means

Which of the following must be true for the conclusion to be true?

(A) Of all the drivers and front-seat passengers in the survey, more than 20 percent were wearing seat belts at the time of their accidents.


Stimulus is saying that 80% were not wearing seat belts, this is saying that less than 80% were NOT wearing seat belts. Does not fit in


(B)Considerably more than 20 percent of drivers and front-seat passengers in Dole County always wear seat belts when traveling by car.

This is about all the drivers. NOT drivers who are injured and surveyed and also restricts the scope to cars from auto accidents.


(C) More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured.


This is saying that front seat passengers and drivers had severe injuries compared to the rear seat P. It is possible that Front seat P & D can reduce risk of injury by wearing seat belts.


(D) More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.

Does not help how we can establish that wearing seat belts will reduce the risk of injury

(E) Most of the auto accidents reported to police in Dole County do not involve any serious injury.

Does not help how we can establish that wearing seat belts will reduce the risk of injury
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Re: CR-Auto accidents [#permalink] New post 12 Jul 2008, 10:12
icandy wrote:
The conclusion above is not properly drawn unless which of the following is true?

This means

Which of the following must be true for the conclusion to be true?

(A) Of all the drivers and front-seat passengers in the survey, more than 20 percent were wearing seat belts at the time of their accidents.


Stimulus is saying that 80% were not wearing seat belts, this is saying that less than 80% were NOT wearing seat belts. Does not fit in


(B)Considerably more than 20 percent of drivers and front-seat passengers in Dole County always wear seat belts when traveling by car.

This is about all the drivers. NOT drivers who are injured and surveyed and also restricts the scope to cars from auto accidents.


(C) More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured.


This is saying that front seat passengers and drivers had severe injuries compared to the rear seat P. It is possible that Front seat P & D can reduce risk of injury by wearing seat belts.


(D) More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.

Does not help how we can establish that wearing seat belts will reduce the risk of injury

(E) Most of the auto accidents reported to police in Dole County do not involve any serious injury.

Does not help how we can establish that wearing seat belts will reduce the risk of injury



Good one Even IMO (C)
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Re: CR-Auto accidents [#permalink] New post 12 Jul 2008, 10:56
MamtaKrishnia wrote:
A recent survey of all auto accident victims in Dole County found that, of the severely injured drivers and front-seat passengers, 80 percent were not wearing seat belts at the time of their accidents. This indicates that, by wearing seat belts, drivers and front-seat passengers can greatly reduce their risk of being severely injured if they are in an auto accident.

Conclusion: Wearing seat belt can reduce the risk of being severly injured.
Premesis: Of severly injured drivers and front seat passengers 80% were not not wearing sealt belt.

Flaw: May be the passengers was seating in rear seat and still got severly injured.

The conclusion above is not properly drawn unless which of the following is true?

(A) Of all the drivers and front-seat passengers in the survey, more than 20 percent were wearing seat belts at the time of their accidents.
(B)Considerably more than 20 percent of drivers and front-seat passengers in Dole County always wear seat belts when traveling by car.
(C) More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured.


(D) More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.
(E) Most of the auto accidents reported to police in Dole County do not involve any serious injury.


"ll go with C
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Re: CR-Auto accidents [#permalink] New post 12 Jul 2008, 11:09
between A and B, choose B because of the word "considerably"

If 50% of drivers/passengers wear seat belts, and that population contributes to only 20% got severely injured, that means that wearing seat belts = less chance of injury than not wearing seat belts.

rule out A because "more than 20%" could mean 21%
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Re: CR-Auto accidents [#permalink] New post 12 Jul 2008, 12:54
Choice C and D both seem doubtful to me.

My choice is A.

C) More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured
Survey states that 80% of front seaters had no seat-belts. But no info about rear seat passanger. Then how do we compare severity of injury between front and rear seat driver? hence cann't be inferred.
D) More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.
More than half of the drivers and front-seat passengers (only those are severely injured not those, who are surveyed) in the survey were not wearing seat belts at the time of their accidents.
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Re: CR-Auto accidents [#permalink] New post 12 Jul 2008, 13:38
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A for me.

Quote:
A recent survey of all auto accident victims in Dole County found that, of the severely injured drivers and front-seat passengers, 80 percent were not wearing seat belts at the time of their accidents. This indicates that, by wearing seat belts, drivers and front-seat passengers can greatly reduce their risk of being severely injured if they are in an auto accident.

The conclusion above is not properly drawn unless which of the following is true?

(A) Of all the drivers and front-seat passengers in the survey, more than 20 percent were wearing seat belts at the time of their accidents.
(B)Considerably more than 20 percent of drivers and front-seat passengers in Dole County always wear seat belts when traveling by car.
(C) More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured.
(D) More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.
(E) Most of the auto accidents reported to police in Dole County do not involve any serious injury.


Argument gives us:

For all drivers and front-seat passengers:

**************************Sev. Injured********************************Not sev. injured
Wear belts_______________20%__________________________________?________
Not wear belts____________80%___________________________________________

So, definitely, if it happens that even less share of those not sev. injured drivers and front-seat passengers wear belts, the conclusion would be false:

For all drivers and front-seat passengers:

**************************Sev. Injured*********************************Not sev. injured
Wear belts_______________20%___________________________________10%
Not wear belts____________80%___________________________________90%

A is the only option that states that such a situation did not take place: if more than
20 percent of all the drivers and front-seat passengers were wearing seat belts, it means that the percentage of those not severely injured but wearing belts was higher than 20%. Thus, wearing belts does indeed reduce their risk of being severely injured to some extent.

Only, even A does not allow to conclude that the risk of being severely injured will be greatly reduced (because % of those not sev. injured who wear belts could as well be, say, 21%). But the other answer choices do not allow to conclude that the risk will be reduced at all – and so, it seems, A is the only suitable option.
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Re: CR-Auto accidents [#permalink] New post 12 Jul 2008, 17:59
greenoak wrote:
A for me.

Quote:
A recent survey of all auto accident victims in Dole County found that, of the severely injured drivers and front-seat passengers, 80 percent were not wearing seat belts at the time of their accidents. This indicates that, by wearing seat belts, drivers and front-seat passengers can greatly reduce their risk of being severely injured if they are in an auto accident.

The conclusion above is not properly drawn unless which of the following is true?

(A) Of all the drivers and front-seat passengers in the survey, more than 20 percent were wearing seat belts at the time of their accidents.
(B)Considerably more than 20 percent of drivers and front-seat passengers in Dole County always wear seat belts when traveling by car.
(C) More drivers and front-seat passengers in the survey than rear-seat passengers were very severely injured.
(D) More than half of the drivers and front-seat passengers in the survey were not wearing seat belts at the time of their accidents.
(E) Most of the auto accidents reported to police in Dole County do not involve any serious injury.


Argument gives us:

For all drivers and front-seat passengers:

**************************Sev. Injured********************************Not sev. injured
Wear belts_______________20%__________________________________?________
Not wear belts____________80%___________________________________________

So, definitely, if it happens that even less share of those not sev. injured drivers and front-seat passengers wear belts, the conclusion would be false:

For all drivers and front-seat passengers:

**************************Sev. Injured*********************************Not sev. injured
Wear belts_______________20%___________________________________10%
Not wear belts____________80%___________________________________90%

A is the only option that states that such a situation did not take place: if more than
20 percent of all the drivers and front-seat passengers were wearing seat belts, it means that the percentage of those not severely injured but wearing belts was higher than 20%. Thus, wearing belts does indeed reduce their risk of being severely injured to some extent.

Only, even A does not allow to conclude that the risk of being severely injured will be greatly reduced (because % of those not sev. injured who wear belts could as well be, say, 21%). But the other answer choices do not allow to conclude that the risk will be reduced at all – and so, it seems, A is the only suitable option.


Hi, Greenoak! This is the most useful approach in CR that I have ever seen. Even I do some math in the same way, but I failed to apply it to CR. This question from OG chellenged me long time ago. Exciting! :-D

Now I can cracked it! Many many thanks!
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Re: CR-Auto accidents [#permalink] New post 12 Jul 2008, 18:03
thanks for providing this information
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Re: CR-Auto accidents [#permalink] New post 13 Jul 2008, 12:21
Thank you, sodenso!
But let’s wait for OA and OE. This ‘greatly reduced’-thing leaves some doubt…
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Re: CR-Auto accidents [#permalink] New post 14 Jul 2008, 23:47
IMO A :

Use rule of negation, If rest of 20% drivers and passangers in the survey were not wearing seat belts, this would weaken the conclusion. Therefore A must be the answer.
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Re: CR-Auto accidents [#permalink] New post 15 Jul 2008, 08:14
OA is B.
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Re: CR-Auto accidents [#permalink] New post 15 Jul 2008, 13:44
After all, it is B… :shock: I can’t believe it…
Could you please provide the OE as well?
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Re: CR-Auto accidents [#permalink] New post 15 Jul 2008, 13:54
MamtaKrishnia wrote:
OA is B.


that's what I thought when i saw the question too. If only 10% of people wear seat belts and they constitute 20% of people with serious injuries -> it's more dangerous to wear seat belts. I'm half joking here.
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Re: CR-Auto accidents [#permalink] New post 15 Jul 2008, 15:17
Quote:
that's what I thought when i saw the question too. If only 10% of people wear seat belts and they constitute 20% of people with serious injuries -> it's more dangerous to wear seat belts. I'm half joking here.


Hi, maratikus. I’m not sure that I understood your point, but that’s what I was thinking:

'The conclusion can’t be true unless B is true' means
'If B is not true, conclusion should be false'.

OK. B is false means: 20% or less of all drivers and front-seat passengers wear belts.

But the conclusion of the argument could still be true with B false. See how:

Imagine that 15% of all drivers and front-seat passengers wear belts. But, for some reason, the percentage of those wearing belts among those who got into accident was 25%, and among those who didn’t was only 10% (seems illogical at first, but nothing in the question prevents us from imagining this situation. Perhaps, greater percentage wears belts on some dangerous roads or whatever). Well, anyway, it seems that we might conclude that for those wearing belts the chance of getting into accident is greater – nothing wrong so far.

However, this does not contradict the argument’s conclusion, which states that wearing belts decrease the risk of injury while already in accident. Because, again, nothing prevents us from imagining the situation when the percentage of those wearing belts among severely injured was 20% (as is given), and among those not severely injured - 30%. So, the conclusion holds: For those who are in accident, wearing belts reduces risk of being severely injured…

It means B is not necessary to make the conclusion true.

What do you think? Perhaps I overlooked smth?
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Re: CR-Auto accidents [#permalink] New post 15 Jul 2008, 15:53
80% of people with serious injuries don't wear seat belts. For example, 100 people had serious injuries, 80 of them didn't wear seat belts, 20 did. Conclusion, if you wear a seat belt -> chances of a serious injury is smaller.

Now let's assume there are 1,000 people driving. 20 with seatbelts, 980 without. All those who wore seatbelts had serious injuries (100% of them), only 80 people out of 980 had serious injuries. Survery results would only be meaningful, if there are more than 20% of people driving with seatbelts. Then conditional probability of a serious injury of people wearing a seatbelt is lower than conditional probability of a serious injury of people not wearing seatbelts.

greenoak wrote:
Quote:
that's what I thought when i saw the question too. If only 10% of people wear seat belts and they constitute 20% of people with serious injuries -> it's more dangerous to wear seat belts. I'm half joking here.


Hi, maratikus. I’m not sure that I understood your point, but that’s what I was thinking:

'The conclusion can’t be true unless B is true' means
'If B is not true, conclusion should be false'.

OK. B is false means: 20% or less of all drivers and front-seat passengers wear belts.

But the conclusion of the argument could still be true with B false. See how:

Imagine that 15% of all drivers and front-seat passengers wear belts. But, for some reason, the percentage of those wearing belts among those who got into accident was 25%, and among those who didn’t was only 10% (seems illogical at first, but nothing in the question prevents us from imagining this situation. Perhaps, greater percentage wears belts on some dangerous roads or whatever). Well, anyway, it seems that we might conclude that for those wearing belts the chance of getting into accident is greater – nothing wrong so far.

However, this does not contradict the argument’s conclusion, which states that wearing belts decrease the risk of injury while already in accident. Because, again, nothing prevents us from imagining the situation when the percentage of those wearing belts among severely injured was 20% (as is given), and among those not severely injured - 30%. So, the conclusion holds: For those who are in accident, wearing belts reduces risk of being severely injured…

It means B is not necessary to make the conclusion true.

What do you think? Perhaps I overlooked smth?
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Re: CR-Auto accidents [#permalink] New post 15 Jul 2008, 15:54
80% of people with serious injuries don't wear seat belts. For example, 100 people had serious injuries, 80 of them didn't wear seat belts, 20 did. Conclusion, if you wear a seat belt -> chances of a serious injury is smaller.

Now let's assume there are 1,000 people driving. 20 with seatbelts, 980 without. All those who wore seatbelts had serious injuries (100% of them), only 80 people out of 980 had serious injuries. Survery results would only be meaningful, if there are more than 20% of people driving with seatbelts. Then conditional probability of a serious injury of people wearing a seatbelt is lower than conditional probability of a serious injury of people not wearing seatbelts.

greenoak wrote:
Quote:
that's what I thought when i saw the question too. If only 10% of people wear seat belts and they constitute 20% of people with serious injuries -> it's more dangerous to wear seat belts. I'm half joking here.


Hi, maratikus. I’m not sure that I understood your point, but that’s what I was thinking:

'The conclusion can’t be true unless B is true' means
'If B is not true, conclusion should be false'.

OK. B is false means: 20% or less of all drivers and front-seat passengers wear belts.

But the conclusion of the argument could still be true with B false. See how:

Imagine that 15% of all drivers and front-seat passengers wear belts. But, for some reason, the percentage of those wearing belts among those who got into accident was 25%, and among those who didn’t was only 10% (seems illogical at first, but nothing in the question prevents us from imagining this situation. Perhaps, greater percentage wears belts on some dangerous roads or whatever). Well, anyway, it seems that we might conclude that for those wearing belts the chance of getting into accident is greater – nothing wrong so far.

However, this does not contradict the argument’s conclusion, which states that wearing belts decrease the risk of injury while already in accident. Because, again, nothing prevents us from imagining the situation when the percentage of those wearing belts among severely injured was 20% (as is given), and among those not severely injured - 30%. So, the conclusion holds: For those who are in accident, wearing belts reduces risk of being severely injured…

It means B is not necessary to make the conclusion true.

What do you think? Perhaps I overlooked smth?
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Re: CR-Auto accidents [#permalink] New post 15 Jul 2008, 16:00
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A - wear seatbelt, not A - don't wear seatbelt, B - injury

P(B*A) = 20%*P(B), P(B*notA) = 80%*P(B)
Statement: P(B|A) < P(B|notA)

P(B*A) = P(B|A)*P(A) -> P(B|A) = P(B*A)/P(A)=20%*P(B)/P(A)
P(B*notA) = P(B|notA)*P(notA) -> P(B*notA)/P(notA)=80%*P(B)/P(B)

Statement: P(B|A) < P(B|notA)
equivalent to 20%/P(A) < 80%/P(notA) equivalent to 0.8*P(A)>0.2*P(notA) since P(notA) = 1-P(A), the initial statement is equivalent to 0.8*P(A) > 0.2*(1-P(A)) -> P(A) > 0.2

Sorry for math
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Re: CR-Auto accidents [#permalink] New post 15 Jul 2008, 17:38
Quote:
A - wear seatbelt, not A - don't wear seatbelt, B - injury

P(B*A) = 20%*P(B), P(B*notA) = 80%*P(B)
Statement: P(B|A) < P(B|notA)

P(B*A) = P(B|A)*P(A) -> P(B|A) = P(B*A)/P(A)=20%*P(B)/P(A)
P(B*notA) = P(B|notA)*P(notA) -> P(B*notA)/P(notA)=80%*P(B)/P(B)

Statement: P(B|A) < P(B|notA)
equivalent to 20%/P(A) < 80%/P(notA) equivalent to 0.8*P(A)>0.2*P(notA) since P(notA) = 1-P(A), the initial statement is equivalent to 0.8*P(A) > 0.2*(1-P(A)) -> P(A) > 0.2

Sorry for math


Many thanks, maratikus; it’s much better with math :)

It seems that we interpreted the argument a bit differently.

I think that P(B|A) < P(B|notA) means that ‘the risk of being severely injured is less for those who wear belts than for those who do not wear belts (regardless of whether they got into accident)’. If the question is interpreted in that way, I completely agree with your reasoning.

However, from the question, it seems that we have to deal with more complex type of conditional probability:

Quote:
A recent survey of all auto accident victims in Dole County found that, of the severely injured drivers and front-seat passengers, 80 percent were not wearing seat belts at the time of their accidents. This indicates that, by wearing seat belts, drivers and front-seat passengers can greatly reduce their risk of being severely injured if they are in an auto accident.


So, it looks like the fact of ‘getting into accident’ is another additional event we need to consider.

We may write:

A - wear seatbelt, not A - don't wear seatbelt
C – got into accident, not C - didn’t get into accident.
B – serious injury, not B – no serious injury.

So, it seems to me that the proper translation of the argument’s conclusion would be P(B|C*A) < P(B|C*not A).

Then, according to the same reasoning as yours:

P(A*B*C) = P(C*B)*0.2
P(notA*B*C) = P(C*B)*0.8

P(B|C*A) = P(A*B*C)/P(C*A) = 0.2*P(C*B)/P(C*A)
P(B|C*notA) = P(notA*B*C)/P(C*notA) = 0.8*P(C*B)/P(C*notA)

The conclusion is equivalent to 0.2/P(C*A) < 0.8/P(C*notA) <=> 0.2*P(C*notA) < 0.8 P(C*A).

Now, since P(C*notA)+P(C*A) = P(C) we have 0.2(P(C) - P(C*A)) < 0.8 P(C*A) which gives us P(C*A) > 0.2*P(C) => P(C*A)/P(C) > 0.2 => P(A|C) > 0.2 (i.e., the probability to have belt when in accident is greater than 0.2 – exactly what option A says)

At the same time, the last inequality does not necessary mean that P(A) > 0.2 (this is what B says).

That’s why in my previous post I gave the example when P(A) = 0.15 (B is false) but P(A|C) = 0.3 (argument is true)…

So, basically, it seems to me that the definition of the correct model that describes this situation depends on how the wording of the argument is interpreted. The line ‘if they are in an auto accident’ made me choose additional event – ‘be in accident’...

Well… I hope you are not bored with this q... :)
What’s your opinion?
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Re: CR-Auto accidents [#permalink] New post 15 Jul 2008, 17:47
greenoak wrote:
Thank you, sodenso!
But let’s wait for OA and OE. This ‘greatly reduced’-thing leaves some doubt…


No matter what is OA! I like that of approach. And it help me out for some other OG-CR like that!

"Learn from the failure" :-D
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Re: CR-Auto accidents   [#permalink] 15 Jul 2008, 17:47
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