2. There are 15 balls in the bag that are identical except for their color, with 10 white balls and 5 red balls. The probability of drawing two balls such that exactly one is white and one is red is $\qquad$ .
2. $\frac{10}{21}$.

The number of ways to draw two balls from the bag is $\mathrm{C}_{15}^{2}=105$, among which the number of ways to draw exactly one white ball and one red ball is $\mathrm{C}_{10}^{1} \mathrm{C}_{5}^{1}=50$. Therefore, the probability of drawing exactly one white ball and one red ball is
$$
\frac{50}{105}=\frac{10}{21} .
$$