Each Chocolate Frog comes with one collectable illustrated wizard card (very cool and not dorky at all, honest). There are equal odds of each card being in a pack (i.e., they have all been produced and distributed evenly). How many packs must we buy in order to have an 80% chance of having obtained all 12 cards? How about 90%? Thanks.
2026-02-24 06:50:30.1771915830
How Many Harry Potter Chocolate Frogs Must I Buy?
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This website on the coupon collector's problem under item 11a (adapted to 12 items from 6) states that the chance you complete your set on purchase $n$ is $\sum_{j=0}^{11} (-1)^j{11 \choose j}\left( \frac {11-j}{12} \right)^{n-1}$ but gives no derivation. You can add up starting with $n=12$ until you get to the desired success probability.