Coupon Collector Problem

number of distinct coupons

50

seed random

1

If a package has one of 50 random baseball cards, how many packages do you need to buy to get a complete set? The expected answer is

50

H

50

≈225

packages, where

H

50

is the harmonic number

1/1+1/2+1/3+…+1/50

. Switching from baseball cards to coupons gives the coupon collector problem: if there are

n

different kinds of coupons and many of them are distributed randomly, the expected number of purchases necessary for a complete set is

n

H

n

.