I'm stuck on this one problem. We have the relative error defined as the square root of the variance divided by the expected value. We need to figure out how big the number of trials has to be in order for the relative error to be smaller than a certain value. For example, if it has to be less than .01, I calculated that:

E(X^2)/(E(X))^2 <= 1.01

(I substituted the definition of variance and was able to get the above statement.)

The events are independent of each other, and the probability that A will happen is p. If X is the frequency of A happening, I have to solve for n.

How do I express E(X^2) and E(X) as something with n and p? Is E(X) just np? If so, what would E(X^2) be? Any help is greatly appreciated.

I think I would start with using the fact that the variance is:
np(1-p), and that E(y)=np