There are 18 yellow and more white and red balls in an urn. How many white and how many red balls are in the urn if the probability of drawing a white or a red ball is $1 / 15$ less than the probability of drawing a white or a yellow ball, and the probability of drawing a red or a yellow ball is $10 \%$ greater than the probability of drawing a white or a yellow ball?

(For the example, see the article 》Elements of Probability Theory《 in this issue.)
Let $x$ be the number of white balls and $y$ be the number of red balls. According to the problem (expressing the individual probabilities as the ratio of favorable to possible cases),

$$
\frac{x+y}{x+y+18}=\frac{x+18}{x+y+18}-\frac{1}{15}
$$

and

$$
\frac{y+18}{x+y+18}=\frac{x+18}{x+y+18} \cdot \frac{11}{10}
$$

Simplifying our system of equations,

$$
\begin{aligned}
x+16 y & =252 \\
-11 y+10 y & =18
\end{aligned}
$$

from which

$$
x=12, \quad y=15
$$

Mecseki Attila (Bp., XV., Dózsa György g. II. o. t.)