[問題]GWD-5-2

[Grace]

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)More than of the 10 employees are women.
(2)The probability that both representatives selected will be men is less than .


Ans: E.

請教這題解題思路 :D Thanks.

[homaru]

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 1/10.

這題是機經喔~....懶得找了:P

設有n個男的,10-n個女的
由(2) C(n,2)/C(10,2)=C(n,2)/45<1/10
當n<=3時,C(n,2)/45<1/10
所以男生有可能0~3個

兩個都是女生的機率:
3個男生,7個女生: C(7,2)/C(10,2)=21/45<1/2
2個男生,8個女生: C(8,2)/C(10,2)=36/45>1/2

都有可能,so E

[Grace]

homaru, Thanks for your help~ ;)

[lisayang83]

想請問一下 為什麼
從題意2
1 - (1/10) 不會是 抽到兩各都是女生的機率呢?
謝謝

[dibert8]

1 - 1/10 也包含了一男一女的機率.

[chris8888]

(1). 女生超過1/2, 表示女生至少6人以上, 使用C(6, 2)/C(10, 2) = 1/3
C(8, 2)/C(10, 2) = 0.6以上 insufficient
(2.) 假設男生n人, C(n, 2)/C(10, 2) = n(n-1) < 9 (經簡化後), n^2-n < 9, 男生人數不可能為小數點, 所以可以代入4,3,2,1,0, 發現當n=3人時, 女生被選機率還是<1/2, 當到達2,1,0時, 就超過1/2了