33. Randomly mixed are seedlings of two tomato varieties: 9 seedlings of the variety White Naliv and 7 - of the variety Verlioka. Find the probability that the first three tomato plants, planted one after another, are seedlings of the variety White Naliv.
S o l u t i o n. The test consists of planting one tomato seedling. Let's consider the events:

$A_{1}$ - the first planted bush is a tomato seedling of the White Naliv variety;

$A_{2}$ - the second planted bush is a tomato seedling of the White Naliv variety;

$A_{3}$ - the third planted bush is a tomato seedling of the White Naliv variety;

$A$ - all three bushes planted one after another are tomato seedlings of the White Naliv variety.

Event $A$ consists in the fact that the first, second, and third bushes are all tomato seedlings of the White Naliv variety. This means that event $A$ is the product of events $A_{1}, A_{2}, A_{3}: A=A_{1} \cdot A_{2} \cdot A_{3}$.

Let's find the probability of event $A$ using the multiplication rule of probabilities. Events $A_{1}, A_{2}, A_{3}$ are dependent, as the probability of each subsequent event (starting from the second) changes depending on whether the previous event occurs or not. According to formula (1), the probability of event $A_{1}$ is $P\left(A_{1}\right)=9 / 16$. The conditional probability of event $A_{2}$, calculated under the condition that event $A_{1}$ has occurred, is $P_{A_{1}}\left(A_{2}\right)=8 / 15$. The conditional probability of event $A_{3}$, calculated under the condition that the previous two events, i.e., events $A_{1}$ and $A_{2}$, have occurred, is $P_{A_{1} A_{2}}\left(A_{3}\right)=7 / 14$. In accordance with formula (14) for $n=3$, we get:

$$
P(C)=P\left(A_{1} A_{2} A_{3}\right)=P\left(A_{1}\right) P_{A_{1}}\left(A_{2}\right) P_{A_{1} A_{2}}\left(A_{3}\right)=\frac{9}{16} \cdot \frac{8}{15} \cdot \frac{7}{14}=0.15
$$