Locked in a dungeon, you are faced with five doors. One of them leads to freedom. The other four will lead you back to the starting room disoriented and confused, so that you will not remember which of the doors you have already tried and have to start again.

How many attempts do you expect to make on the average (statistically) before making it out?

(In reply to

re: Solution by TomM)

You'd use the same basic approach for "Trading cards", but that problem is a good deal harder. Essentially, you have to figure out the probability that buying the nth pack of cards completes your set, then do a big honking summation to find the expected value. I haven't devoted enough brain cycles to that problem to figure out what that probability is, much less how to add all the terms together.