2011-I-14

$\begin{array}{cl}
= & \dfrac{9}{12} \times \dfrac{5}{6} + \dfrac{3}{12}\times \dfrac{2}{3} \\
= & \dfrac{19}{24}
\end{array}$

1. The required probability

   $\begin{array}{cl}
   = & \dfrac{5}{6} \times \dfrac{2}{3} \\
   = & \dfrac{5}{9}
   \end{array}$

2. The required probability

   $\begin{array}{cl}
   = & \dfrac{3}{12}\times \dfrac{2}{3} \times \dfrac{2}{11} \times \dfrac{2}{3} \\
   = & \dfrac{2}{99}
   \end{array}$

3. The probability that two customers do not complain

   $\begin{array}{cl}
   = & \dfrac{9}{12}\times \dfrac{5}{6} \times \dfrac{8}{11} \times \dfrac{5}{6} + 2 \times \dfrac{9}{12}\times \dfrac{3}{11} \times \dfrac{5}{9} + \dfrac{2}{99} \\
   = & \dfrac{62}{99} \\
   > & \dfrac{1}{2}
   \end{array}$

   Therefore, the probability of not making complaints by the two selected customers is greater than the probability of making complaints by both of them.