I know that "at least"-probabilities can be calculated as: $p(\ge m) = 1 - p(<m)$ and for small values of $m$, say 2, this becomes $p(\ge 2) = 1 - (p(0) + p(1))$.
But now I am given a problem where I am asked to calculate the probability of at least 10 successes out of 70 trials. I doubt that I should do this by brute-force, calculating $1 - \sum_{i=0}^{9}{p(i)}$.
In the given problem there is a fixed probability of success per trial of $\frac{1}{5}$.
Are there alternative ways of calculating the "at least" / "at most" probabilities in such a scenario?