Coupon Collector's Problem
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Tap a term to see what it means, or .
Calculate
Example: an album of 670 stickers, sold in packs of 5, all equally common. Without swapping with anyone, how many do you need to buy, on average, to complete it? Change the values to work out your own case.
Step by step
What each term means
- Expected Purchases (E[T])
- How many stickers you buy, on average, until you have all N different ones.
- Album Size (N)
- How many different stickers there are.
- Harmonic Number (Hₙ)
- With j already in the album, the next new one takes, on average, N/(N − j) purchases. Adding all the waits gives N times this sum, which grows like ln N + 0.577.