OK, guys, I'm new here. I'll start posting a problem that apparently I'm unable to solve...

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

S1withnsymbols (or elements)

S2with(n-r)symbols (or elements)

each of the symbols composing the two strings has independent probabilitypof having value '1'.

So, the question is: what's the probability of having more symbols with value '1' inS2than inS1?

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 lotfor anyone willing to help here!