help 抽波仔(概率)

P(白) = 4/15

P(藍) = 1/5

P(紅) = 8/15

設白波為 x 分, 則抽一個波的期望值得分為:

4x/15 + 16/15 - 4/5

如要公平, 則此值應為零:

4x/15 + 16/15 - 4/5 = 0

4x/15 = -4/15

x = -1

即白波為 -1 分 (扣 1 分)

2010-03-03 15:23:10 補充：
4x/15 + 16/15 - 4/5 = 0

4x/15 + 16/15 - 12/15 = 0

4x/15 + 4/15 = 0

(4/15)x = -4/15

x = -1

please define what 公平 is?

does it mean the expexted 分 = 0?

2010-03-04 09:13:23 補充：
If yes, then....

Pr (白波) = 4 / 15
Pr (藍波) = 3 / 15 = 1 / 5
Pr (紅波) = 8 / 15

E (分) = 白波分 x Pr (白波) + 藍波分 x Pr (藍波) + 紅波分 x Pr (紅波) = (4 / 15) x 白波分 - 4 x (1 / 5) + 2 x (8 / 15) = (4 / 15) x 白波分 + (4 / 15) = 0

Hence, 白波分 = -1

抽到白波扣1分