Pr i mer 7. For the normal operation of the car base, there should be no less than eight cars on the line, and there are ten of them. The probability of each car not coming out on the line is 0.1. Find the probability of the normal operation of the car base for the next day.
Solution. The car base will work normally (event $D$) if eight (event $A$), nine (event $B$), or all ten (event $C$) cars go out on the line. According to the theorem of the addition of probabilities,

$$
P(D)=P(A)+P(B)+P(C)=P_{10}(8)+P_{10}(9)+P_{10}(10)
$$

Each term will be found using the Bernoulli formula.

Since the probability of each car not going out on the line is 0.1, the probability of a car going out on the line will be 0.9, i.e., $p=0.9, q=0.1$. From the condition, it follows that $n=10, k=8,9,10$. Therefore,

$$
\begin{gathered}
P(D)=C_{10}^{8} \cdot(0.9)^{8} \cdot(0.1)^{2}+C_{10}^{9} \cdot(0.9)^{9} \cdot 0.1+C_{10}^{10} \cdot(0.9)^{10} \cdot(0.1)^{0} \approx \\
\approx 0.1937+0.3874+0.3487=0.9298
\end{gathered}
$$