About five years ago, a Newsweek review of the then new iPod raised a concern that the shuffle feature might not be random. The author noted that of the 3,000 songs in his playlist, 3 tracks from the same album on more than one occasion ended up in his 120 song autofill: “This seemed to defy the odds,”, he opined.
Now I'm sure there were many algebraic calculations by probabilists hither and yon on the likelihood of those iPod occurrences after the article's publication. Several professors from the highly-rated statistics department at Iowa State University, in contrast, offered a different yet quite simple analysis using computer simulation rather than mathematics to arrive at their conclusion. Assuming that the 3,000 tune playlist was apportioned across 250 “albums”, with 12 songs per album, the authors deployed the R statistical package to generate 10,000 trials of 120-case random samples against a 250*12 vector consisting of 12 1's, 12 2's,....,12 250's -- tracking how many yielded three or more “album” hits. Just under 9,500 of the 10,000 trials met the criteria – almost 95%! Rather then an aberration, the 3+ album runs were the norm. And rather than torture themselves with probability calculations, the professors had simply finessed an estimate using easily accessible computer power.
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