题目
(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(AB)C,overline(AB)C,Aoverline(B)U 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)).
(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$A\cup B,\overline{AB},A\cup B\cup C,\overline{AB}C,\overline{AB}C,A\overline{B}U C$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$P(\overline{AB})$.
题目解答
答案
(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 $P(\overline{AB} \overline{C}) = \frac{3}{20}$
⑤ $P(\overline{AB} C) = \frac{7}{60}$
⑥ $P(\overline{AB} \cup C) = \frac{7}{20}$
(3)
(i) $P(\overline{AB}) = \frac{1}{2}$
(ii) $P(\overline{AB}) = \frac{3}{8}$
\[
\boxed{
\begin{array}{ll}
(1) & \frac{5}{8} \\
(2) & \frac{11}{15}, \frac{4}{15}, \frac{17}{20}, \frac{3}{20}, \frac{7}{60}, \frac{7}{20} \\
(3) & \frac{1}{2}, \frac{3}{8}
\end{array}
}
\]