I am taking a course related to probabilities and as a primer we are given some word problems, I have somehow slipped by in my earlier classes and never have taken a classes on such subjects. I was hoping for some direction on how I might go about solving this problem. The problem is stated as such
A mischievous student wants to break into a computer file, which is password-protected. Assume that there are $n$ equally likely passwords, and that the student chooses passwords independently at at random and tries them. Let $N_n$ be the number of trials required to break into the file. Determine the probability density function of $N_n$
(a) If unsuccessful passwords are not eliminated from further selections.
(b) If unsuccessful passwords are eliminated from further selections.
So just talking it through, for the student to crack the password after $x$ tries he would have the chance of $x / n$ meaning the more times he tries the better chance he has to crack the password, because once $x = n$ then the password has to be cracked.
So as a function, the probability that the password is cracked after $x$ tries would be
$$ P( N_n = x) \ = \ x / n$$
I think that this would be the solution to part b of the problem above because this takes into account that the student can assume past unsuccessful attempts will never work again?
But I am lost for insight on part a, as to how unsuccessful attempts would affect his future attempts?
Can anyone offer some guidance on this problem?