Example 3. Evaluate the probability that in 3600 independent throws of a die, the number of times 6 points appear will be no less than 900.
Solution. Let $X$ be the number of occurrences of 6 points in 3600 tosses, then $M(X)=3600 \cdot \frac{1}{6}=600$. Using inequality (4.1.2.) with $a=600, \delta=900$:

$$
P(X \geq 900) \leq \frac{600}{900}=\frac{2}{3}
$$