There are 2 white balls, 4green balls and 3 blue balls in a box. If three balls are drawn one after another with replacement, find the probability that all the balls have the same colour.
我知道有人答如下:
P(all the balls have the same colour)
=P(GGG)+P(WWW)+P(BBB)
=64/729+(2/9)^3+(3/9)^3
=11/81
但我唔明點解可以WWW呢?
only 2 white balls!!!
但11/81係岩....
有時間請到我的發問,我仲有一條唔明....
f5 maths!!!!!!!
2008-09-05 6:39 am
回答 (3)
2008-09-05 7:08 am
✔ 最佳答案
There are 2 white balls, 4green balls and 3 blue balls in a box. If three balls are drawn one after another with replacement, find the probability that all the balls have the same colour.我知道有人答如下:
P(all the balls have the same colour)
=P(GGG)+P(WWW)+P(BBB)
=64/729+(2/9)^3+(3/9)^3
=11/81
但我唔明點解可以WWW呢?
only 2 white balls!!!
但11/81係岩....
因為with replacement, 所以當第1 個是white , 就加番1 個white, 於是第2 個抽到white 既機會又係 2/9. 如是者, 第3 個抽到white 既機會又係 2/9.
結果, 2/9＊2/9＊2/9
2008-09-05 7:15 am
條數係咪話 抽出後既ball放回個box度? 如果係既話,,,
同時抽出三個ball同一顏色既概率均如下:
第一次抽到G後再放回box,,第二次抽到又係g之後又放回box度,,第三次抽到G後又係放回box度,, 形成 P(GGG)
注意:同時抽出三粒ball既意思係 "第一次抽既係G,,第二次抽中又係G,,第三次抽中又係G"
至於點解可以P(WWW),,,這是因為你第一次抽一粒W出黎之後再放回BOX度,,然後再抽,,再放回BOX,,再抽,,, 但係個BOX度既BALL既總數依然不變,,所以W自然沒有少,,,
因為有可能3次都抽到G, 3次都抽到W, 3次都抽到B
所以我地會把佢地既概率全部 +晒佢
即 P(GGG or WWW or BBB)
同時抽出三個ball同一顏色既概率均如下:
第一次抽到G後再放回box,,第二次抽到又係g之後又放回box度,,第三次抽到G後又係放回box度,, 形成 P(GGG)
注意:同時抽出三粒ball既意思係 "第一次抽既係G,,第二次抽中又係G,,第三次抽中又係G"
至於點解可以P(WWW),,,這是因為你第一次抽一粒W出黎之後再放回BOX度,,然後再抽,,再放回BOX,,再抽,,, 但係個BOX度既BALL既總數依然不變,,所以W自然沒有少,,,
因為有可能3次都抽到G, 3次都抽到W, 3次都抽到B
所以我地會把佢地既概率全部 +晒佢
即 P(GGG or WWW or BBB)
2008-09-05 7:07 am
with replacement ma ..
white balls drawn are replaced with another white one
white balls drawn are replaced with another white one
參考: myself
收錄日期: 2021-04-16 23:17:19
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080904000051KK02531