7. A real numbers $x$ is randomly chosen in the interval $\left[-15 \frac{1}{2}, 15 \frac{1}{2}\right]$. Find the probability that the closest integer to $x$ is odd.
Solution: By using a graphical method, we can see that, for real $x$ on $\left[-n-\frac{1}{2}, n+\frac{1}{2}\right]$, $n$ an even integer, the probability that the closest integer to $x$ is odd is $\frac{n}{2 n+1}$. The desired probability is $\left(\frac{15}{31}\right)$.