We have two strings (or sets, if you prefer):

*S1*with

*n*symbols (or elements)

*S2*with

*(n-r)*symbols (or elements)

each of the symbols composing the two strings has independent probability

*p*of having value '1'.

So, the question is: what's the probability of having more symbols with value '1' in

*S2*than in

*S1*?

I need the formula. As simple as it may seem, I am absolutely lost in this. I tried to make a summation of the probability mass function in some way but quickly I realized that I wasn't going anywhere. So...

**thanks a lot**for anyone willing to help here!