12. 樣本空間個數\(3^n\)
事件個數\(\displaystyle \frac{3^n+3(-1)^n}{4}\)
一般化機率\(\displaystyle \frac{3^n+3(-1)^n}{4\times 3^n}\)

計算2
由\(\displaystyle sinB=\frac{AF}{AH} \Rightarrow \overline{AH}=\frac{bcosA}{sinB}\)

且\(\displaystyle tanB=\frac{CD}{DH}=\frac{bcosC}{tanB} \Rightarrow \overline{DH}=\frac{bcosBcosC}{sinB}\)

所求\(\displaystyle \frac{AH}{DH}=\frac{cosA}{cosBcosC}=\frac{-cos(B+C)}{cosBcosC}=tanBtanC-1\)