中五數學一問（續概率） 十分題目

20.
B = 白朗勝出， B' = 白朗沒有勝出， K = 家宜勝出
P(B) = 1/3
P(B') = (1/2) + (1/6) = 2/3
P(K) = 1/2


(a)
所求的概率
= P(B, B, B)
= P(B) x P(B) x P(B)
= (1/3)³
= 1/27


(b)
P(B', B', B')
= P(B') x P(B') x P(B')
= (2/3)³
= 8/27

所求的概率
= 1 - P(B', B', B')
= 1 - (8/27)
= 19/27


(c)
所求的或然率
= P(K, B, K) + P(B, K, B)
= P(K) x P(B) x P(K) + P(B) x P(K) x P(B)
= (1/2) x (1/3) x (1/2) + (1/3) x (1/2) x (1/3)
= (1/12) + (1/18)
= (3/36) + (2/36)
= 5/36