30. In the green cutting department of the fruit experimental station, 20 green cuttings were prepared for planting in the greenhouse, including 8 cuttings of winter-hardy apricot variety 9-114, and the rest are cuttings of plum variety Eurasia 21. Three cuttings were randomly selected. Find the probability that at least one of them is an apricot cutting.
S o l u t i o n. This problem is of the same type as problem 29. For its rational solution, we recommend applying the method considered in the second part of problem 29.

Consider the events:

$A$ - at least one plum cutting is selected;

$\bar{A}$ - no plum cutting is selected.

The probability of event $\bar{A}$ is

$$
P(\bar{A})=\frac{C_{12}^{3}}{C_{20}^{3}}=\frac{11}{57}
$$

Event $\bar{A}$ is the opposite of event $A$, therefore, according to formula (11), the required probability is

$$
P(A)=1-P(\bar{A})=1-\frac{11}{57}=\frac{46}{57} \approx 0.8070
$$