## 5. Black and White Balls

An urn contains 5 white and 5 black balls. Then, 3 balls are randomly drawn one by one. This is done in two ways: 1 - the drawn ball is returned to the urn, 2 - the balls are not returned. In which of these two cases is there a higher probability of drawing one white and two black balls?
5. In the first case (drawing a ball with replacement), we have:

$P_{\mathbf{i}}=$ (number of variants where one of the three balls is white) $\times 1 / 2^{3}=3 / 8=9 / 24$.

In the second case (drawing without replacement), we get:

$P_{2}=$ [number of ways to choose one (white) ball from five $\times$ number of ways to choose two (black) balls from five]: number of ways to choose three balls from ten

$$
\left(C_{5}^{1} \cdot C_{5}^{2}\right): C_{10}^{3}=5 / 12=10 / 24
$$

Thus, in the second case, the desired result is slightly more probable than in the first.