投擲兩枚勻稱骰子,求所擲得的兩點數之和為質數的概率。

2009-04-19 2:26 am
投擲兩枚勻稱骰子,求所擲得的兩點數之和為質數的概率。

A 1/2

B 5/11

C 5/12

D 7/18

已知 answer 為C,但我不知點計,希望大家可以教教我。

回答 (1)

2009-04-19 3:31 am
✔ 最佳答案

每粒骰 1 點至 6 點,所以兩粒骰共有 36 個排列:
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

其和為質數,共有 15 個排列:
(1, 1) → 2 點
(1, 2) (2, 1) → 3 點
(1, 4) (4, 1) (2, 3) (3, 2) → 5 點
(1, 6) (6, 1) (2, 5) (5, 2) (3, 4) (4, 3) → 7 點
(5, 6) (6, 5) → 11 點

概率
= 15/36
= 5/12
=


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