Question 26
The amount $2.5$ is split into two nonnegative real numbers uniformly at random, for instance, into $2.143$ and $0.357,$ or into $\sqrt3$ and $2.5-\sqrt3.$ Then each number is rounded to its nearest integer, for instance, $2$ and $0$ in the first case above, $2$ and $1$ in the second. What is the probability that the two integers sum to $3?$