Last sticker to complete the album

Question

A sticker album needs 12 distinct stickers, each equally likely and independent per pack. You collect until the album is full. One sticker is the captain.

What is the probability that the captain is the very last sticker you complete the album with?

Accepted Answer

Each of the 12 stickers appears with the same probability on every pack, so no sticker is inherently "harder." The stickers are interchangeable in the collection process. By symmetry, all 12 are equally likely to be the last new sticker, so P(	ext{captain is last}) = \frac{1}{12} \approx 0.0833. This holds even though the captain might feel rare: rarity here is only about equal draw chances, and all are equal. Takeaway. For n equally likely types, the last-to-appear probability is \frac{1}{n} for every type, independent of any labels or feelings about which is "special."

Last sticker to complete the album

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