In reply to:


> Actually it's only approximately 1 in 720,000

Oops, yeah, you got me. I was going under the assumption that those were his FIRST three songs, which is, of course, not what he actually said. Apparently Bruno was not the only to mis-read the post. All that math knowledge won't do me any good if I can't solve the correct equation. And I always considered word problems to be one of my skills.

Hmm, but let me explore your solution a little bit more thoughly. Your example works IF the FIRST song is one of the Pollys. Then the chances of the next song being Polly would indeed be 1 / 600. But if the first Polly was played half way through, then the chance of the next one being Polly would only be 1 / 300.



Good points. Let's look at this a different way. Say that there are n songs in the playlist, k of which are Polly. Then there are exactly C(n,k) = n!/(n-k)!k! ways to distribute the k Polly's among the n songs, and there are n-k+1 ways to place k consecutive Polly's in n songs. Plugging in n=1200 and k=3 gives us a probability of 1198/287280400 or 1/239800.

All assuming all shuffles are equally probable which we know isn't the case (due to Empeg bugginess and the limitations of psuedorandom generators). BTW, I've had two versions of the same Tori Amos song pop up in a row which surprised me quite a bit. But now that I've done the math it doesn't seem quite so unusual.

And, just as a counter example to Tony's claim, I've actually cycled through my 1400+ song playlist multiple times. I was doing a *lot* of driving last fall.

--John