1588. What is the probability of event $A$ occurring in each trial, if the most probable number of occurrences of event $A$ in 120 trials is 32?
Solution. Here $n=120, m_{0}=32$. According to inequality (1),

$$
120 p-(1-p) \leqslant 32 ; 120 p+p \geqslant 32
$$

Solving the obtained system, we find that $\frac{32}{121} \leqslant p \leqslant \frac{33}{121}$.