Does the answer that the probability is $\dfrac{\pi}{12}$ make sense? If not, I can explain that portion more.

Assuming that we understand the answer is $\dfrac{\pi}{12}$ let's deal with the $P$ and $Q$ part. We want the answer to be in the form $\dfrac{P\times \pi}{Q}$. Note $\dfrac{\pi}{12} = \dfrac{1\times \pi}{12}$ meaning that $P = 1$ and $Q = 12$. Therefore, $Q - P = 12 - 1 = 11$ as our answer.