There's some sticker albums meant for collections (example: Panini FIFA World Cup), which there's a number of, let's say, 500 stickers. So while you get more stickers the easier to get the same sticker (for our example, would be the same Player), those stickers are no use and must be changed/sold. So at the end you end up buying a lot more than just 500 stickers !.
What is the formula (or function, cumulative distribution function, ....) to know, given two numbers:
A: how many (stickers) do you currently have.
B: what is the total (500 in our example).
C: the probability that the next sticker would be different. So 1-C is the probability that the next sticker is an 'already-have'.
Question 1: What is the probability that the next one would be an 'already-have' sticker ?. If A = 0 then P = 0, if A = 500 then P = 1
Question 2: How many stickers would I have to buy if A is 0 to fill the album ?
Question 3: is there any website with an online calculator ? I found for small values, but not for big values.
Question 4: at what time does C < 1-C ?.