17. Closed Rural Store (8th grade. 3 points). At noon, Anna Kuzminichna looked out the window and saw Klava, the store clerk, leaving for a break. At two minutes past one, Anna Kuzminichna looked out the window again and saw that no one was in front of the closed store. Klava was absent for exactly 10 minutes, and when she returned, she found Ivan and Foma standing by the door, with Foma clearly arriving later than Ivan. Find the probability that Foma had to wait for the store to open for no more than 4 minutes.
Solution. It is reasonable to assume that the arrival time of each customer is uniformly distributed over the permissible interval. This can be understood as: the probability of arrival at each minute (or second) is the same. More precisely - the probability of arrival in some time interval is proportional to the duration of this interval.

Let's measure time in minutes from noon, taking it as 0, and denote $x$ as the time of Ivan's arrival, and the time of Foma's arrival as $y$.

According to the condition, $2 < x < y < 10$. Let's represent the corresponding figure in the coordinate system $x O y$. We get a triangle $A B C$.

We need to find the probability of the event $(x \geq 6)$. Mark it on the diagram and we will see that inside the triangle it is represented by the trapezoid $E B C D$. In different ways, it is easy to find that

$$
\mathrm{P}(x \geq 6)=\frac{S_{E B C D}}{S_{A B C}}=\frac{3}{4}
$$

![](https://cdn.mathpix.com/cropped/2024_05_06_bb47797e9df8f4bc3d4dg-22.jpg?height=765&width=765&top_left_y=254&top_left_x=1154)

Answer: 0.75.