Compound experiment with NNIV

Let X be a non-negative integer valued random variable. Observe X items and mark each of the X items independently with probability s where $\displaystyle 0<s<1$. What is the probability that all X items are marked?

Solution so far:

On the surface it looks like $\displaystyle Pr[all \ items \ marked ] = s^X $, but I know there is no way this can be this easy... What am I doing wrong?

Re: Compound experiment with NNIV

Hello,

Your mistake is that you're not considering X as a random variable.

What you can compute is P(all items marked|X=x)=s^x

But if you want the probability, not the conditional one, just remember that E[X]=E[E[X|Y]] (and that a probability is an expectation).

Thus P(all items marked)=E[P(all items marked|X)]=E[s^X]