2 populations are independently surveyed using s.r.s of size n, and 2 proportions, p1 and p2, are estimated. It is expected that both population proportions are close to 0.5. What should the sample size be so that the standard error of the difference, $\displaystyle \hat p_1-\hat p_2$ will be less than 0.02?

I can find $\displaystyle \sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}(\frac{N-n}{N-1})}$ for the individual component, but I don't know how to apply for $\displaystyle \hat p_1-\hat p_2$.

Answer is 1250.