求NN解答。。。。。过程

unimelb86

In an insurance company, each policy has a paper record or an electric record, or both of them. 60 percent of the policies having incorrect paper record have incorrect electric record and 75 percent of the policies having incorrect electric record have incorrect paper record. 3 percent of all the policies have both incorrect paper and incorrect electric records. If we randomly pick out one policy, what is the probability that it is one having both correct paper and correct electric record?


answer: 94%

完全不懂。。。求解

zelda爱star

为啥我算的不对==
我怎么算出来是91%？这道题也太绕了吧==

unimelb86

zelda爱star

不是NN，把我的想法写一下吧，也让NN们指出我的问题所在==
先解释下我的运算符号==
incorrect paper--坏p, correct paper--好p
首先题目说60%的坏p是坏e, 75%的坏e是坏p,而既是坏p又是坏e的是全体的3%。
所以设整体是a，坏p是x,坏e是y
0.6x=0.75y=0.03a
解出来x=5%a
        y=4%a
所以说好p是95%a, 好e是96%a
然后又因为好p 好e一共是1
所以既是好p又是好e的就是95%+96%-100%=91%

backlighting

x=5%a
y=4%a
我觉得对的。
但是，坏p+好p=a?  会不会出现，有e但无p的情况？
          坏e+好e=a      那有p无e得情况呢
这个，我有点晕

sdcar2010

category: correct   incorrect
P                a         100-a
E                b         100-b

Both P and E correct: x
P correct but E incorrect: c
P incorrect but E correct: d
Both P and E incorrect: 3

Then:
total: x+c+d+3=100
P incorrect: 100-a=d+3
E incorrect: 100-b=c+3
60% of incorrect P have incorrect E:  0.6*(100-a) = 3
75% of incorrect E have incorrect P:  0.75*(100-b) = 3

Five unknowns, five equations to solve. From the last two equations: a = 95; b=96.
Adding the first three equations, you get: x+100-a-b =3
Therefore x=94

cycyang

Many thankx for the very clear explanation, as you do in other sections!

sandychen168

category: correct   incorrect
P                a         100-a
E                b         100-b

Both P and E correct: x
P correct but E incorrect: c
P incorrect but E correct: d
Both P and E incorrect: 3

Then:
total: x+c+d+3=100
P incorrect: 100-a=d+3
E incorrect: 100-b=c+3
60% of incorrect P have incorrect E:  0.6*(100-a) = 3
75% of incorrect E have incorrect P:  0.75*(100-b) = 3

Five unknowns, five equations to solve. From the last two equations: a = 95; b=96.
Adding the first three equations, you get: x+100-a-b =3
Therefore x=94

-- by 会员 sdcar2010 (2011/3/20 20:57:17)

Many thanks to this solution, but I still doubt it. Because the question says " each policy has a paper record or an electric record, or both of them." and you only consider 4 situations, and that is every record have both paper and electric records, either correct or incorrect. I think you fail to consider this situation "what about a policy has only a paper record but NO electric record?"

sdcar2010

True. I think the assumption is that No Record = Having an incorrect record. Otherwise, this question is too complicated.

category: correct   incorrect
P                a         100-a
E                b         100-b

Both P and E correct: x
P correct but E incorrect: c
P incorrect but E correct: d
Both P and E incorrect: 3

Then:
total: x+c+d+3=100
P incorrect: 100-a=d+3
E incorrect: 100-b=c+3
60% of incorrect P have incorrect E:  0.6*(100-a) = 3
75% of incorrect E have incorrect P:  0.75*(100-b) = 3

Five unknowns, five equations to solve. From the last two equations: a = 95; b=96.
Adding the first three equations, you get: x+100-a-b =3
Therefore x=94

-- by 会员 sdcar2010 (2011/3/20 20:57:17)

Many thanks to this solution, but I still doubt it. Because the question says " each policy has a paper record or an electric record, or both of them." and you only consider 4 situations, and that is every record have both paper and electric records, either correct or incorrect. I think you fail to consider this situation "what about a policy has only a paper record but NO electric record?"

-- by 会员 sandychen168 (2011/10/17 0:12:34)

sandychen168

True.

But keep in mind that final answer should be applied to either cases. So choosing a specific, easier scenario to work with would save you some time during the exam.

category: correct   incorrect
P                a         100-a
E                b         100-b

Both P and E correct: x
P correct but E incorrect: c
P incorrect but E correct: d
Both P and E incorrect: 3

Then:
total: x+c+d+3=100
P incorrect: 100-a=d+3
E incorrect: 100-b=c+3
60% of incorrect P have incorrect E:  0.6*(100-a) = 3
75% of incorrect E have incorrect P:  0.75*(100-b) = 3

Five unknowns, five equations to solve. From the last two equations: a = 95; b=96.
Adding the first three equations, you get: x+100-a-b =3
Therefore x=94

-- by 会员 sdcar2010 (2011/3/20 20:57:17)

Many thanks to this solution, but I still doubt it. Because the question says " each policy has a paper record or an electric record, or both of them." and you only consider 4 situations, and that is every record have both paper and electric records, either correct or incorrect. I think you fail to consider this situation "what about a policy has only a paper record but NO electric record?"

-- by 会员 sandychen168 (2011/10/17 0:12:34)

-- by 会员 sdcar2010 (2011/10/17 0:26:34)

Totally agree with you! But in this case, I think we cannot work this problem out if we should consider the "What if a policy has only paper record but NO electric record" situation. Because we don't know what the proportion of those situations is. We only can get the total propotion. Therefor, I think we can never reach a exact conclusion about the question, and I think maybe there are some little mistakes in this question because the statement is not sufficient enough to work the problem out.