# How to find the number of trials given the success probability and variance?

If X has a binomial distribution how do you find the number of trials given a success probability and the variance? I'm lost. Could I just divide the variance by the success probability?

• I cannot parse the sentence “Number of trials given a success probability and the variance”. Can you copy exactly the problem, maybe with some math typesetting? – Nap D. Lover Sep 19 '19 at 20:10

The variance is $$\sigma^2=np(1-p)$$, so substitute $$p$$ and $$\sigma^2$$ into this and rearrange for $$n$$, i.e. $$n=\frac{\sigma^2}{p(1-p)}.$$