洗完澡突然来了灵感，写下这个一直以来让我的头脑模糊不清的逻辑题的思路。
过去做错过这个题，也看过解释，也取过非来验证假设，还是思路不是很清晰。
尝试学习NN大侠 SDCAR2010的建议，尽量用E文来写，try to think in English.
请SDCAR2010有空的话点评一下我的思路。
其实，有时候把问题抽象了看，反而更清晰。很多逻辑题里面各种细节词汇绕来绕去反而分散了注意力。
去芜存菁，才能抓住问题的本质。
A recent report determined that although only 3 percent of drivers on Maryland highways equipped their vehicles with radar detectors, 33 percent of all vehicles ticketed for exceeding the speed limit were equipped with them. Clearly, drivers who equip their vehicles with radar detectors are more likely to exceed the speed limit regularly than are drivers who do not.
The conclusion drawn above depends on which of the following assumptions?
(A) Drivers who equip their vehicles with radar detectors are less likely to be ticketed for exceeding the speed limit than are drivers who do not.
(B) Drivers who are ticketed for exceeding the speed limit are more likely to exceed the speed limit regularly than are drivers who are not ticketed.
(C) The number of vehicles that were ticketed for exceeding the speed limit was greater than the number of vehicles that were equipped with radar detectors.
(D) Many of the vehicles that were ticketed for exceeding the speed limit were ticketed more than once in the time period covered by the report.
(E) Drivers on Maryland highways exceeded the speed limit more often than did drivers on other state highways not covered in the report.
For express articulately and simply, following abbreviations used:
DR = Driver whose car is equiped with radar NDR = Driver whose car is not equiped with radar
Firstly, let's think in an abstract way
PREMISE:
In a group of DRs & NDRs, DRs 3% and NDR 97%
In a subgroup with performance XXX, DRs 33% and NDR 67%
Conclusion:
DRs are likely to perform YYY than NDRs
Reasoning:
Because DR's ratio is higher than NDR's ratio in the subgroup, (THEREFORE), if the subgroup is tending to perform YYY, we can conclude that DRs are more tending to perform YYY than NDRs. The higher the DR's ratio in the subgroup, the more DRs are tending to perform.
QUESTION:
What is the assumption?
Obviously, the assumption is that all members of the subgroup are likely to perform YYY
The Group = all drivers of Maryland.
The Subgroup=those drivers who were ticketed for exceeding the speed limit.
XXX = exceeding the speed limit
YYY= exceeding the speed limit regularly
XXX and YYY are different things in logic. 作者: honpont2013 时间: 2011-11-14 21:41
(THEREFORE), if the subgroup is tending to perform YYY
Not very clear what the above sentence means. I thought that you
want to say "In the subgroup, NDR is more likely to perform XXX
than DR."作者: littlebluesks 时间: 2011-11-15 06:32
Nope
I exactly mean that " if the subgroup is tending to perform YYY, we can conclude that DRs are more tending to perform YYY than NDRs."
In the whole group, the ratio of DRs are far lower than NDRs, whereas in the subgroup the ratio of DRs is much greater than that in the whole group.
For some specific example,
The group = all people in the world
The ratio of Japanese man in the whole group = 3%
The subgroup = smokers (people who smokes; ie. XXX=smoking)
The ratio of Japanese men in the subgroup =33%
if we have a premise that the smokers are likely to get the lung cancer than other people. (YYY=getting the lung cancer)
We can conclude that Japanese men are more likely to get the lung cancer than other people.
If the ratio of Japanese man in the subgroup increases to 90%
We can conclude that Japanese men are much, much, much, ..., much more likely to get the lung cancer than other people.作者: honpont2013 时间: 2011-11-19 06:32
Reasoning:
Because DR's ratio is higher than NDR's ratio in the subgroup, (THEREFORE), if the subgroup is tending to perform YYY, we can conclude that DRs are more tending to perform YYY than NDRs. The higher the DR's ratio in the subgroup, the more DRs are tending to perform.
Just based on the logic chain shown above, "the subgroup is tending to perform YYY" is a sufficient assumption, but might not be a necessary one for the argument.
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