Example 5. The germination rate of seeds of this variety of plants is $80 \%$. What is the probability that out of 5 sown seeds, at least 4 will germinate.
Solution. According to the condition $p=0.8$, therefore $q=0.2$. Further, $n=5, k \geq 4$, i.e., $k$ takes the values 4 or 5. Let the event whose probability we need to determine be denoted by $A$, then $P(A)=P_{5}(4)+P_{5}(5)$. According to the Bernoulli formula, we find the probabilities $P_{5}(4), P_{5}(5)$ and their sum

$$
\begin{aligned}
P(A)= & P_{5}(4)+P_{5}(5)=\frac{5!}{4!1!} \cdot(0.8)^{4} \cdot 0.2+(0.8)^{5}= \\
& =5 \cdot 0.4096 \cdot 0.2+0.32768=0.73728 .
\end{aligned}
$$