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
(a) all the balls are green
(b) two are white and one is green
(c) all the balls have the same colour.
probability
2007-11-02 5:54 am
回答 (2)
2007-11-02 6:13 am
✔ 最佳答案
G:Green, W:White, B:Blue(a)
P(all the balls are green)
=P(GGG)
=(4/9)^3
=64/729
(b)
P(two are white and one is green)
=P(WWG)+P(WGW)+P(GWW)
=2/9*2/9*4/9+2/9*4/9*2/9+4/9*2/9*2/9
=16/243
(c)
P(all the balls have the same colour)
=P(GGG)+P(WWW)+P(BBB)
=64/729+(2/9)^3+(3/9)^3
=11/81
2007-11-02 5:00 pm
a) P(all balls are green) = 4/9 x 4/9 x 4/9 = 64/729
b) P(two are white and one is green) = 3C2 x 2/9 x 2/9 x 4/9 = 16/243
c) P(all balls have same colour) = P(all balls are white) + P(all balls are green) +
P(all balls are blue)
= 2/9 x 2/9 x 2/9 + 64/729 + 3/9 x 3/9 x 3/9
= 11/81
b) P(two are white and one is green) = 3C2 x 2/9 x 2/9 x 4/9 = 16/243
c) P(all balls have same colour) = P(all balls are white) + P(all balls are green) +
P(all balls are blue)
= 2/9 x 2/9 x 2/9 + 64/729 + 3/9 x 3/9 x 3/9
= 11/81
收錄日期: 2021-04-23 22:17:29
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https://hk.answers.yahoo.com/question/index?qid=20071101000051KK03960