求助:GWD新题m02

fuchaoyang

Q2:

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 ATH connecttype="rect" gradientshapeok="t" extrusionok="f">ATH>?

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

(2) The probability that both representatives selected will be men is less than 1/10

这题选E,怎么推导的啊?

saibei008

假设男的有n个，女的有m个。m+n=10。

p=c(m,2)/c(10,2)=m(m-1)/(10*9); p>1/2 => m>=8

(1) => m>=5，不充分

(2) c(n,2)/c(10,2)=n(n-1)/(10*9)<1/10 => n<=3 => m>=7 还是不充分

fuchaoyang

p=m(m-1)/(10*9)>1/2怎么能推出m>=8? 这个不等式不是只能推出m^2-m>45么？

请再指导！

linlin2008

当M=7时,M^2-M&lt;45,M=8时即可

kenlily

m是整数，你一个个数字代进去就可以了。