解:
(1)根據(jù)題意,列表如下:
| 轉(zhuǎn)盤(pán)A\轉(zhuǎn)盤(pán)B | 2 | 4 | 6 |
| ---- | ---- | ---- | ---- |
| 1 | (1,2) | (1,4) | (1,6) |
| 2 | (2,2) | (2,4) | (2,6) |
| 3 | (3,2) | (3,4) | (3,6) |
| 4 | (4,2) | (4,4) | (4,6) |
所有可能得到的點(diǎn)P的坐標(biāo)為:(1,2),(1,4),(1,6),(2,2),(2,4),(2,6),(3,2),(3,4),(3,6),(4,2),(4,4),(4,6)。
(2)由列表可知,共有12種等可能的結(jié)果,計(jì)算各點(diǎn)對(duì)應(yīng)的$s = x + y$:
(1,2):$s = 1 + 2 = 3$
(1,4):$s = 1 + 4 = 5$
(1,6):$s = 1 + 6 = 7$
(2,2):$s = 2 + 2 = 4$
(2,4):$s = 2 + 4 = 6$
(2,6):$s = 2 + 6 = 8$
(3,2):$s = 3 + 2 = 5$
(3,4):$s = 3 + 4 = 7$
(3,6):$s = 3 + 6 = 9$
(4,2):$s = 4 + 2 = 6$
(4,4):$s = 4 + 4 = 8$
(4,6):$s = 4 + 6 = 10$
其中$s\lt6$的結(jié)果有(1,2)、(1,4)、(2,2)、(3,2),共4種。
$\therefore P(\text{甲獲勝})=\frac{4}{12}=\frac{1}{3},$$P(\text{乙獲勝}) = 1 - \frac{1}{3}=\frac{2}{3}。$
$\because \frac{1}{3}\neq\frac{2}{3},$$\therefore$這個(gè)游戲不公平,對(duì)乙有利。