Example 17. In an urn, there are 6 blue and 4 red balls. Two balls are drawn in succession. What is the probability that both balls are blue?
Solution. Let event $A$ be "drawing a blue ball on the first draw", and event $B$ be "drawing a blue ball on the second draw". We need to find the probability of event $A B$. Since

$$
\begin{gathered}
P(A)=\frac{6}{10}=\frac{3}{5} \\
P(B / A)=\frac{6-1}{10-1}=\frac{5}{9}
\end{gathered}
$$

$$
P(A B)=P(A) \cdot P(B / A)=\frac{3}{5} \cdot \frac{5}{9}=\frac{1}{3}
$$