1. Boris distributes 8 white and 8 black balls into two boxes. Nastya randomly chooses a box and then takes a ball from it without looking. Can Boris distribute the balls in such a way that the probability of drawing a white ball is greater than $\frac{2}{3}$?
Answer. Yes.

Solution. Boris will put 1 white ball in the first box, and all the others in the second. Then the probability of drawing a white ball is $\frac{1}{2}+\frac{1}{2} \cdot \frac{7}{15}=\frac{22}{30}>\frac{2}{3}$.

Comment. Correct solution - 20 points. Correct solution with arithmetic errors - 15 points. Considered a special case where the balls are distributed equally - 5 points. Solution started but progress is insignificant - 1 point. Only the correct answer without a solution - 0 points.