How to derive sum of $\left(\frac{X_i}{Y_i}\right)$ probability with Gamma distribution?

Question

I would like to derive this probability:

$p = Pr\left\{\displaystyle \frac {X_1}{Y_1} + \frac{X_2}{Y_2} + \dots + \frac{X_n}{Y_n} \gt a\right\}$, $a$ is a positive constant. All $X_i$ and $Y_i$, $i=1..n$, are independent and follow the Gamma distribution.

Would anyone suggest me a way to derive the probability $p$ above? Thank you very much.