64. In the reading room, there are six textbooks on probability theory, three of which are in hardcover. The librarian randomly took two textbooks. Find the probability that both textbooks will be in hardcover.
Solution. Let's introduce the notation for events: $A$ - the first textbook has a cover, $B$ - the second textbook has a cover. The probability that the first textbook has a cover, $P(A)=3 / 6=1 / 2$.

The probability that the second textbook has a cover, given that the first taken textbook was in a cover, i.e., the conditional probability of event $B$, is: $P_{A}(B)=2 / 5$.

The required probability that both textbooks have covers, according to the multiplication theorem of probabilities, is

$$
P(A B)=P(A) \cdot P_{A}(B)=1 / 2 \cdot 2 / 5=0.2 .
$$