Lost in probability...

May 2010
OK, guys, I'm new here. I'll start posting a problem that apparently I'm unable to solve... (Shake)

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!