The box contains 30 balls in white and 5 in black. From the box they take at random 2 balls one after the other.

The box contains 30 balls in white and 5 in black. From the box they take at random 2 balls one after the other. Find the probability that both balls will turn out to be black.
There are 30 + 5 = 35 balls in the box.
Consider the following events: A – the first ball will be black. B – the second ball will also be black.
The probability of an event A such that the first ball is black:
P (A) = 5/35.
If a black ball is taken out, then 34 balls remain in the box, 4 of them are black.
The conditional probability of occurrence of an event B such that the second ball will also be black:
P (B) = 4/34.
By the probability multiplication theorem, we have:
P (AB) = P (A) P (B) = 5/35 4/34 = 0.0168.
Answer: The probability that both balls will turn out to be black is 0.0168.