There are 2 balck balls and 3 white balls in a bag. 4 balls are drawn at randomly without replacement . What is the probability that 2 black balls and 2 white balls are drawn?
我要解釋....
更新1:
myisland8132答得都唔錯, 但係我只一個中三學生... 可唔可以用中文+埋唔好用咁多專有名詞~
probability難題XDD
2008-12-24 7:19 am
好難呀-.-
There are 2 balck balls and 3 white balls in a bag. 4 balls are drawn at randomly without replacement . What is the probability that 2 black balls and 2 white balls are drawn?
我要解釋....
There are 2 balck balls and 3 white balls in a bag. 4 balls are drawn at randomly without replacement . What is the probability that 2 black balls and 2 white balls are drawn?
我要解釋....
回答 (2)
2008-12-25 10:19 am
✔ 最佳答案
將抽到的可能性全部相加便行，抽到的次序有6個可能性，括號內為抽到的機會率：1) BBWW (2/5 x 1/4)
2) BWBW (2/5 x 3/4 x 1/3)
3) BWWB (2/5 x 3/4 x 2/3 x 1/2)
4) WBBW (3/5 x 2/4 x 1/3) (與第2個情況有相同機會率)
5) WBWB (3/5 x 2/4 x 2/3 x 1/2) (與第3個情況有相同機會率)
6) WWBB (3/5 x 2/4 x 2/3 x 1/2) (與第3個情況有相同機會率)
將以上情況相加：
(1) + (2) + (3) + (4) + (5) + (6)
= (2/5 x 1/4) + 2(2/5 x 3/4 x 1/3) + 3((3/5 x 2/4 x 2/3 x 1/2)
= 1/10 + 1/5 + 3/10
= 6/10
= 3/5 (或0.6)
抽到兩個黑波及兩個白波的機會率是3/5。
參考: 自己計算
2008-12-24 7:52 am
This is a question about hypergeometic distribution
The total combinations to draw 4 balls from 5 balls are
5C4=5
The total combinations to draw 2 black balls and 2 white balls from 2 balck balls and 3 white balls are (2C2)(3C2)=3
So the required probability is
3/5
The total combinations to draw 4 balls from 5 balls are
5C4=5
The total combinations to draw 2 black balls and 2 white balls from 2 balck balls and 3 white balls are (2C2)(3C2)=3
So the required probability is
3/5
收錄日期: 2021-04-25 16:58:34
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081223000051KK02083