Probability of picking from categories with repeated trys

Maybe this is a stupid question but I can't seem to find any examples of this scenario on the internet. If you can direct me to somewhere this type of problem is solved that would be helpful. :)

There are 9 blue balls and 11 red balls in a jar. If you pick n balls from the jar, with replacement, what is the probability of picking at least m red balls in terms of m and n.

It looks like a simple binomial question. The probability of picking exactly k red balls is $\binom{n}{k}(\frac{11}{20})^k (\frac{9}{20})^{n-k}$ To get what you want, sum k from m to n.