My roommates and I were looking at dutch redband treasure chest candies link for the candy. One pack contains 14 chests with candy as treasure inside. On the face of every chest is 1/12th of a treasure map displayed. in other words, when you have 12 distinct pieces of the map, you have completed the "puzzle". We were wondering, what is the probability that you receive a full map in one pack?
We assume that:
- the supplier does fill the packs randomly and
- the supplier has an infinite supply of every map piece
So as a more general problem: We have a 12 sided dice, which is thrown 14 times. What is the probability that we get each face of the dice at least once.
