Question about Chernoff bounds

guest5123 · science forum beginner Joined: 17 Apr 2006 Posts: 1

Hi,
I need to use the Chernoff bound P(X<= gamma*n*p) for binomial
distribution
there seem to be several versions. One appears in books and etc. and it
says

P(X<= gamma*n*p)<=exp{-(1-gamma)^np/2}

and the other in Wikipedia and several sites that copied from it, and
it says

P(X> gamma*n*p)>exp{-n/(2(p-1/2)^2)}

These two versions seem very different. Is the wikipedia version
correct?
Can someone point me to a proof of it?

Thanks a lot

Google