Example 1. A pocket contains 10 white balls and 8 black balls. 4 balls are drawn from it. Find: (1) the probability of drawing exactly 2 white balls; (2) the probability of drawing at most 2 white balls.
(1) Omitted. (2) From a bag containing 10 white balls and 8 black balls, 4 balls are drawn.
Let event $\mathrm{A}$: exactly 2 white balls,
Event B: exactly 1 white ball,
Event C: no white balls (all black balls).
Then $\mathrm{P}(\mathrm{A})=\frac{\mathrm{C}_{10}^{2} \cdot \mathrm{C}_{8}^{2}}{\mathrm{C}_{18}^{4}}=\frac{7}{17}$,
$$
\begin{array}{l}
P(B)=\frac{C_{10}^{1} \cdot C_{8}^{3}}{C_{18}^{4}}=\frac{28}{153}, \\
P(C)=\frac{C_{8}^{4}}{C_{18}^{4}}=\frac{7}{306} .
\end{array}
$$
$\because$ Events A, B, and C are mutually exclusive,
$$
\begin{array}{l}
\therefore \mathrm{P}(\mathrm{A}+\mathrm{B}+\mathrm{C}) \\
=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})+\mathrm{P}(\mathrm{C})=\frac{21}{34} .
\end{array}
$$