Example 6.4. It is known that a phone call should follow between 11:00 and 11:30. What is the probability that the call will occur in the last 10 minutes of the specified period, if the moment of the call is random?
Solution. We will use a geometric scheme. For this, the time interval from 11:00 to 11:30 will be represented as a segment $A B$ 30 units long, and the time interval from 11:20 to 11:30 - as a segment $C B$ 10 units long (Fig. 70). The

![](https://cdn.mathpix.com/cropped/2024_05_22_e915d089cc29fd681be5g-288.jpg?height=128&width=663&top_left_y=1445&top_left_x=393)

Fig. 70

random ringing at some moment within the considered half-hour is represented by a randomly chosen point on the segment $A B$. Then the probability that the ringing will occur in the interval from 11:20 to 11:30, in the obtained scheme, means the probability that
a point randomly chosen on the segment $A B$ will belong to the segment $C B$. This probability is obviously equal to:

$$
p=\frac{10}{30}=\frac{1}{3} \text {. }
$$