M1 further probability

2013-02-06 12:20 pm

Two players A and B regularly play chess together. When A has the first move in a game, the probability of A winning the game is 0.5 and the probability of B winning the game is 0.3. When B has the first move, the probability of B winning the game is 0.3 and the probability of A winning the game is 0.2.

ignore this : Given that A and B toss a fair coin to decide who has the first move in a game, find the probability of the game ending in a draw.

To add some more fun to the games, A and B agree to change the way of determining who has the first move in a game. Under the new way, the probability of A having the first move in any game is p. If A and B have equal chance of winning a game.

1. find the value of p. answer = 1/3
2. find the probability of A winning the game. answer = 0.3
3. find the probability of a game ending in a draw. answer = 0.4

答案應該係點計? 列出步驟, thank you

回答 (1)

50418129

2013-02-06 4:46 pm

✔ 最佳答案

(1)

the probability of A having the first move = p
the probability of B having the first move = 1 - p
the probability of A wins = (p)(0.5) + (1 - p)(0.2)
the probability of B wins = (p)(0.3) + (1 - p)(0.3)
thus, (p)(0.5) + (1 - p)(0.2) = (p)(0.3) + (1 - p)(0.3)
0.5p + 0.2 - 0.2p = 0.3p + 0.3 - 0.3p
0.3p = 0.1 => p = 1/3

(2)

the probability of A wins
= (p)(0.5) + (1 - p)(0.2)
= (1/3)(0.5) + (1 - (1/3))(0.2)
= 0.3

(3)

the probability of a game ending in a draw
= 1 - the probability of A wins - the probability of B wins
= 1 - the probability of A wins - the probability of A wins
= 1 - 0.3 - 0.3
= 0.4

參考: knowledge

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