Example 24. In the box, there are 15 balls, of which 5 are blue and 10 are red. Two balls are drawn sequentially from the box; the first ball is not returned to the box. Find the probability that the first ball drawn will be blue and the second will be red.
Solution. Let $A$ be the event "the first ball is blue", and $B$ the event "the second ball is red". From the condition, we have

$$
P(A)=\frac{5}{15}=\frac{1}{3}, \quad P(B / A)=\frac{10}{14}=\frac{5}{7}
$$

According to the first of the formulas (1.8.8), we get

$$
P(A B)=P(A) P(B / A)=\frac{5}{15} \cdot \frac{10}{14}=\frac{5}{21} \approx 0.238
$$