gwd-18-15 一个NN解释了，貌似对了，但还是有问题的

Q15:

Fact: Asthma, a bronchial condition, is much less common ailment than hay fever, an allergic inflammation of the nasal passages.

Fact: Over 95 percent of people who have asthma also suffer from hay fever.

If the information given as facts above is true, which of the following must also be true?

A.
            Hay fever is a prerequisite for the development of asthma.

B.
            Asthma is a prerequisite for the development of hay fever.

C.
            Those who have neither hay fever nor asthma comprise less than 5 percent of the total population.

D.
            The number of people who have both of these ailments is greater than the number of people who have only one of them.

E.
            The percentage of people suffering from hay fever who also have asthma is lower than 95 percent.

FACT1: P(A)<(F)

FACT2: P(F|A)=P(AF)/P(A) >95%

SO: P(A|F)=P(AF)/P(F)< P(AF)/P(A)<95%-->E

我也觉得这样推导有问题。

1.P(F|A)=P(AF)/P(A) >95%没问题，

2.P(A|F)=P(AF)/P(F)，

   因为P(A)<(F) ，

   所以P(AF)/P(A) > P(AF)/P(F)没问题，

结合1.P(AF)/P(A) >95%

不必然推出 P(AF)/P(F) < 95%啊，因为P(AF)/P(F)有可能=95%啊。。。

另外：

以上是我的理解，不知道对否。。。

Asthma , is much less common ailment than hay fever

Over 95 percent of people, who have asthma, also suffer from hay fever

Or to say 95% of asthma people have fever

Ask: how many % of Hey fever people has asthma?

Make a small circle for Asthma;

Make a big circle for Hay fever;

They have common intersection area, and mark it with gray color.

If the intersection area is 95% of Asthma, the small circle, it is for sure less than 95% of Hay fever, the big circle.

Conclusion, the percentage for people having both type of diseases constitute bigger percentage for the the uncommon disease as for the more common diseases.