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擲3顆公正的骰子，任兩顆和為7的機率？

Sep 22nd 2013, 03:15

Ans: 任兩顆和為7的機率=0

說明:
令a,b,c為1~6的正整數.
a + b = 7 ...(1式)
b + c = 7 ...(2式)
c + a = 7 ...(3式)
任兩顆和為7的意義即為(1式)(2式)(3式)同時成立.
亦即解這3式的聯立方程式.
(1式)-(3式)得 b - c = 0 ...(4式)
(2式)+(4式)得 2b=7
即b=3.5, 所以此聯立方程式無整數解.
也就是任兩顆和為7的可能組合不存在.
故任兩顆和為7的機率=0

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