A woman has n keys, of which one will open her door. (a) if she tries the keys at random, discarding those that do not work, what is the probability that she will open the door one her kth try? (b) what if she does not discard previously tried keys?
This one is instructive if you do it in your imagination:
Of course one of the keys out of the n is going to open the door so the probability at ...
This solution is provided in approximately 124 words. It uses a simple explanation as to how to find probability.