Anikó and Béla agreed that they would sit on the bench in the schoolyard for 10 minutes each. Independently of each other, they randomly choose a time between $12^{00}$ and $12^{50}$ to sit down. What is the probability that they will meet?
Suppose Anikó arrives at the meeting place at 12 o'clock $x$ minutes, and Béla arrives at 12 o'clock $y$ minutes. Let's represent this event by the point $(x, y)$ in the plane! Since $x$ and $y$ can be any points in the interval $[0,50]$, the set of all events is the square $0 \leqslant x \leqslant 50,0 \leqslant y \leqslant 50$.

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The meeting will occur if $|x-y| \leqslant 10$, that is, $x-10 \leqslant y \leqslant x+10$. We have marked this set on the diagram with hatching.

Since $x$ and $y$ are chosen independently, the probability we are looking for is the ratio of the area of the hatched part to the area of the entire square:

$$
P=\frac{t}{T}=\frac{50^{2}-2 \cdot\left(\frac{1}{2} \cdot 40^{2}\right)}{50^{2}}=\frac{900}{2500}=\frac{9}{25}=36 \%
$$