Average # of tracks that must be heard on a CD, whose player's shuffle function can play the same song >1×, before all tracks of CD heard.

Question

Suppose you have a CD of $n$ tracks. Your CD player's shuffle function is broken; it selects a random song, possibly even the one(s) already played, before all tracks are played. How many tracks (possibly duplicates), on average, does one need to listen to to hear every song at least once?

The solution to this problem is $n H(n)$ where $H(n)$ is the n$^\mathrm{th}$ harmonic number.

How is this derived?

This is essentially the same as the coupon collector's problem — Mark Bennet, Mar 14 '14 at 15:05
@MarkBennet: I've never heard of that problem. Thanks for letting me know! — Geremia, Mar 14 '14 at 15:06
essentially? this IS the coupon collector's problem. Or maybe CD track collector's problem. — Guy, Mar 14 '14 at 15:08

score 0 · Accepted Answer · answered Mar 14 '14 at 17:38

0

This is the coupon collector's problem.

answered Mar 14 '14 at 17:38

Geremia

2,511

Average # of tracks that must be heard on a CD, whose player's shuffle function can play the same song >1×, before all tracks of CD heard.

1 Answers1