155. What is the probability \( p \) of an event occurring in each of 49 independent trials, if the most probable number of occurrences of the event in these trials is 30?
Solution. According to the condition, $n=49, k_{0}=30$. We will use the double inequality $n p-q \leqslant k_{0}30, \quad 49 p-(1-p)0,6$. From the second inequality of the system, we find $p \leqslant 0,62$.

Thus, the required probability must satisfy the double inequality $0,6<p \leq 0,62$.