3.(1)设A,B,C是三个事件，且P(A)=P(B)=P(C)=1/4，P(AB)=P(BC)=0， P(AC)=1/8,求A,B,C至少有一个发生的概率.(2)已知P(A)=1/2,P(B)=1/3,P(C)=1/5,P(AB)=1/10,P(AC)=1/15,P(BC)= 1/20,P(ABC)=1/30,求Acup B,overline(AB),Acup Bcup C,overline(ABC),overline(ABC),overline(A B) cup C的概率.(3)已知P(A)=1/2,(i)若A,B互不相容,求P(overline(AB)),(ii)若P(AB)=1/8,求P(overline(AB)).

(1) $P(A \cup B \cup C) = \frac{1}{4} + \frac{1}{4} + \frac{1}{4} - 0 - 0 - \frac{1}{8} + 0 = \frac{5}{8}$。 答案：$\boxed{\frac{5}{8}}$ (2) ① $P(A \cup B) = \frac{11}{15}$ ② $P(\overline{AB}) = \frac{4}{15}$ ③ $P(A \cup B \cup C) = \frac{17}{20}$ ④ $P(\overline{A} \overline{B} \overline{C}) = \frac{3}{20}$ ⑤ $P(\overline{A} \overline{B}C) = \frac{7}{60}$ ⑥ $P(\overline{A} \overline{B} \cup C) = \frac{7}{20}$ (3) ① $P(\overline{AB}) = \frac{1}{2}$ ② $P(\overline{AB}) = \frac{3}{8}$ \[ \boxed{ \begin{array}{ll} (1) & \frac{5}{8} \\ (2) & \frac{11}{15}, \frac{4}{15}, \frac{17}{20}, \frac{3}{20}, \frac{7}{60}, \frac{7}{20} \\ (3) & \frac{1}{2}, \frac{3}{8} \\ \end{array} } \]