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shayuamerica

If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2?

(1)     More than 1/2 of the 10 employees are women.

(2)     The probability that both representatives selected will be men is less than .

                  

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

How to figure out E?

tonynotears

从10个雇员里面随机选2个，p是选出的2个人是女人的概率。

条件一 超过一半的人都是女人

条件二 选出2个是男人的概率小于选出2个是女人的概率

设一共有X个女人，条件1可以推出，C(2,X)/C(2，10)=p，且X>5;可以得出P>2/9;

条件2，楼主没给出完整叙述，如果给了一个数的话，那比一比是不是和上面推出的条件有什么关系就知道；

如果给的是“选出的2个为男人的概率比选出的女人的概率小”，那么就不用算了，条件1都说了超过一半的人是女人，当然选中为女的概率大，所以条件2成了废话，于是选E

shayuamerica

2,The probability that both representatives selected will be men is less than1/10

复制过来的时候不知道这里不兼容!

zacharyzhang

Here I explain why 2 alone is not enough if "The probability that both representatives selected will be men is less than1/10"

The total number of select 2 different people is 45 (10*9/2). When the probability is less than 1/10, we know there are at most 3 men because 4*3/2=6 > 4.5. 
While the left 7 women means 7*6/2 =21 < 45/2.  (This is to say only when there are more than 8 women will cause probobability>1/2)