152. How many independent trials with a probability of the event occurring in each trial equal to 0.4 are needed so that the most probable number of occurrences of the event in these trials is 25?
Solution. According to the condition, $k_{0}=25 ; p=0.4 ; q=0.6$. We will use the double inequality

$$
n p-q \leqslant k_{0}25
$$

From the first inequality of the system, we find $n24.6 / 0.4=61.5$.

Thus, the required number of trials must satisfy the double inequality $62 \leqslant n<64$.