h*********n
发帖数: 278 | 1 Consider a game with 2 players, A and B. Player A has 8 stones, player B has
6. Game proceeds as follows. First, A rolls a fair 6-sided die, and the
number on the die determines how many stones A takes over from B. Next, B
rolls the same die, and the exact same thing happens in reverse. This
concludes the round. Whoever has more stones at the end of the round wins
and the game is over. If players end up with equal # of stones at the end of
the round, it is a tie and another round ensues. What is the probability
that B wins in 1, 2, ..., n rounds? ”
我现在算出来
(1)第一轮赢是10/36
(2)第一轮平是5/36
(3)第二轮赢given第一轮平是15/36
(4)第二轮平given第一轮平是1/6
所以第n轮赢得概率是5/36 * (1/6)^(n-2) * 15/36
现在不解的是，网上有人给出的（3）是13/36而不是15/36，别的都一样。到底是我错
了还是网上错了？
谢谢！ | N*****a
发帖数: 250 | 2 我觉得你的是对的啊。
has
of
【在 h*********n 的大作中提到】
: Consider a game with 2 players, A and B. Player A has 8 stones, player B has
: 6. Game proceeds as follows. First, A rolls a fair 6-sided die, and the
: number on the die determines how many stones A takes over from B. Next, B
: rolls the same die, and the exact same thing happens in reverse. This
: concludes the round. Whoever has more stones at the end of the round wins
: and the game is over. If players end up with equal # of stones at the end of
: the round, it is a tie and another round ensues. What is the probability
: that B wins in 1, 2, ..., n rounds? ”
: 我现在算出来
: (1)第一轮赢是10/36
| a*******e
发帖数: 253 | 3 第一轮平的概率是怎么算出来的？
has
of
【在 h*********n 的大作中提到】
: Consider a game with 2 players, A and B. Player A has 8 stones, player B has
: 6. Game proceeds as follows. First, A rolls a fair 6-sided die, and the
: number on the die determines how many stones A takes over from B. Next, B
: rolls the same die, and the exact same thing happens in reverse. This
: concludes the round. Whoever has more stones at the end of the round wins
: and the game is over. If players end up with equal # of stones at the end of
: the round, it is a tie and another round ensues. What is the probability
: that B wins in 1, 2, ..., n rounds? ”
: 我现在算出来
: (1)第一轮赢是10/36
|
|
