145. Each of the 15 elements of a certain device is tested. The probability that an element will withstand the test is 0.9. Find the most probable number of elements that will withstand the test.
Solution. According to the condition, $n=15, p=0.9, q=0.1$. Let's find the most probable number $k_{0}$ from the double inequality

$$
n p-q<k_{0}<n p+p
$$

Substituting the data from the problem, we get

$$
15 \cdot 0.9-0.1 \leqslant k_{0}<15 \cdot 0.9+0.9, \text{ or } 13.5 \leqslant k_{0}<14.4 \text{. }
$$

Since $k_{0}$ is an integer and since there is only one integer between 13.4 and 14.4, namely 14, the most probable number $k_{0}=14$.