FeiFei 6-1 还是概率

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

Key: 94%

我觉得94%是或者correct paper 或者correct electric 或者both的概率,而非both correct paper and correct electric, 题目中并不知道both correct paper and correct electric在整个record的百分比,请牛牛指点

设：一共policies=n

the policies having incorrect paper record 用ip表示

the policies having incorrect electric record 用ie表示

好了，依题意，60%ip=75%ie=3%n

得ip=5%n

ie=4%n

所以the policies having incorrect paper record 和the policies having incorrect electric record（这两部分中都包含both incorrect paper and incorrect electric records）的总数是ip+ie-3%n=6%n

所以both correct paper and correct electric record的是除了上述的，等于94%n，故概率是94%

伐好意思,还是么理解,去掉6% 的IP和IE, 剩下的94%是正确的P or E or P&E呀,因为题目中说each policy has a paper record or an electric record, or both of them.怎么能知道这94%肯定是又有P又有E (both of them)呢

呵呵，这个地方是这样的。

ip包括 （p不对但e对）和（p不对且e也不对）

ie包括 （e不对但p对）和（p不对且e也不对）

楼主所说的正确的P不就是（e不对但p对）么，已经包含在ie中了；同理e正确的就是（p不对但e对）包含在ip里了，所以94%只包含e和p同时都对的了。

这回解释明白没？

这类题目，简直就是考Verbal，抓住几点：

1）60% of the policies having incorrect paper record have incorrect electric record 

——纸件记录不正确的，有60%的可能性其电子记录也是不正确的；

2）75% of the policies having incorrect electric record have incorrect paper record.

——电子记录不正确的，有75%的可能性其纸件记录也是不正确的；

3）3% of all the policies have both incorrect paper and incorrect electric records

——所有记录中，有3%纸件记录与电子记录都不正确。

解题：假设共有100条policies，那么有3条policies的纸件记录与电子记录都不正确。

由1）可知，这3条policies只占‘纸件记录不正确的’之60%，因此，‘纸件记录不正确的’共有3/60% = 5条；

由2）同理可知，‘电子记录不正确的’共有3/75% = 4条；

综上，记录有错的policies共有 5+4-3=6（集合A+B-AB）,于是‘没有任何错误的’policies有100-6=94条。

因此，抽到‘没有任何错误的’policies的概率为94%。

（直接用比例算也可以，直接假设共有100条，个人觉得简单一些 ^_^）

对不起楼主，明白你的意思了。

由于each policy has a paper record or an electric record, or both of them.所以94%中应该包括having both correct paper and correct electric record（同时含有）和 只有paper而且是correct，和只有electric而且correct。

这样根据题里给的条件是无法确定having both correct paper and correct electric record。