65. In the first urn, there are 6 black and 4 white balls, in the second - 5 black and 7 white balls. One ball is drawn from each urn. What is the probability that both balls will be white?
Solution. Let $A_{1}$ be the event that a white ball is drawn from the first urn; $A_{2}$ be the event that a white ball is drawn from the second urn. Obviously, events $A_{1}$ and $A_{2}$ are independent. Since $P\left(A_{1}\right)=4 / 10=2 / 5, P\left(A_{2}\right)=7 / 12$, then by formula (5) we find

$$
P\left(A_{1} A_{2}\right)=\frac{2}{5} \cdot \frac{7}{12}=\frac{14}{60}=\frac{7}{30}
$$