8. A station has exactly one bus arriving between $8:00 \sim 9:00$ and $9:00 \sim 10:00$ every morning, but the arrival times are random, and the two arrival times are independent of each other, as shown in Table 1. A passenger arrives at the station at $8:20$. What is the expected waiting time for the passenger (rounded to the nearest minute)?
Table 1
\begin{tabular}{|l|c|c|c|}
\hline Arrival time $8:10 \sim 9:10$ & $8:30 \sim 9:30$ & $8:50 \sim 9:50$ \\
\hline Probability & $\frac{1}{6}$ & $\frac{1}{2}$ & $\frac{1}{3}$ \\
\hline
\end{tabular}
8. 27 .

The distribution of passenger waiting times is shown in Table 2.
Table 2
\begin{tabular}{|c|c|c|c|c|c|}
\hline \begin{tabular}{c} 
Waiting Time \\
(min)
\end{tabular} & 10 & 30 & 50 & 70 & 90 \\
\hline Probability & $\frac{1}{2}$ & $\frac{1}{3}$ & $\frac{1}{6} \times \frac{1}{6}$ & $\frac{1}{2} \times \frac{1}{6}$ & $\frac{1}{3} \times \frac{1}{6}$ \\
\hline
\end{tabular}

The mathematical expectation of the waiting time is
$$
\begin{array}{l}
10 \times \frac{1}{2}+30 \times \frac{1}{3}+50 \times \frac{1}{36}+ \\
70 \times \frac{1}{12}+90 \times \frac{1}{18} \doteq 27
\end{array}
$$