Given the average of 50 requests per second and X measuring the number of "successes" in a given second long time interval given a Poission distribution
\begin{equation*}
f(x) = \frac{50^x}{x!}e^{-50}.
\end{equation*}
Then,
\begin{equation*}
P(X \lt 50) = F(49) = \sum_{x=0}^{49} \frac{50^x}{x!} e^{-50}
\end{equation*}
and using the graphing calculator function poissoncdf(50,49) = 0.48119.