推 dogdog915:got it! thanks:) 08/20 13:53
※ 引述《dogdog915 (Lyndi)》之銘言：
: 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.
: 答案是E
: (1) 我知道女性至少6個, 所以P= C(6,2) / C(10,2) = 1/3 -->insufficient
: 請問(2)該如何解呢?
: 謝謝!
Let w be the number of female employees, then (10-w) is the number of male
employees. Note that w is a non-negative whole number and is no more than 10.
According to the description of the question, we have to know whether
w 10-w
C x C
2 0 w(w-1) 1
p = -------------- = ---------- > ---
10 10 x 9 2
C
2
<=> w(w-1) > 45 ?
<=> w is more than or equal to 8 ?
<=> w = 8 or 9 or 10 ?
(1) alone gives us w > 5
=> not sufficient! {for example, p < 1/2 if w = 6 and p > 1/2 if w = 8}
10-w w
C x C
2 0 (10-w)(10-w-1) (10-w)(9-w) 1
(2) alone implis that --------------- = ---------------- = ------------- < ----
10 10 x 9 90 10
C
2
=> (10-w)(9-w) < 9
=> w = 7 or 8 or 9 or 10
=> not sufficient! {for example, p < 1/2 if w = 7 and p > 1/2 if w = 8}
(1) & (2) together give us w = 7 or 8 or 9 or 10
=> not sufficient! {for example, p < 1/2 if w = 7 and p > 1/2 if w = 8}
Thus you have to choose (E).
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