1537. In an urn, there are 5 white and 4 black balls. Two balls are drawn in succession. Find the probability that both balls are white.
Solution. Let $A_{1}$ be the appearance of a white ball on the first draw, and $A_{2}$ be the appearance of a white ball on the second draw. We are interested in the event $A_{1} A_{2}$. By the multiplication theorem of probabilities,

$$
P\left(A_{1} A_{2}\right)=P\left(A_{1}\right) P\left(A_{2} / A_{1}\right)=\frac{5}{9} \cdot \frac{5-1}{9-1}=\frac{5}{9} \cdot \frac{1}{2}=\frac{5}{18}=0.278 .
$$