Mike Anderson Wrote: > ...I frequently find that a random mix will select two songs off the > same album within a short span of songs, even though I have quite a few > albums (more than 600)... Despite having a mathematics degree, I too was initially suckered by the birthday paradox and was surprised by the frequency of multiple tracks from a single album in a random playlist. To recover my pride, since someone mentioned the birthday paradox (http://en.wikipedia.org/wiki/Birthday_paradox), I could resist doing the calculations. Here are some probabilities for seeing at least two tracks from the same album (any album, not a particular album) for a collection of 350 albums (my collection) and 650 (Mike's).
350 albums, playlist with assuming replacement (individual tracks may repeat) 10 tracks, probability 12.2% 20 tracks, probability 42.5% 30 tracks, probability 72.2% 40 tracks, probability 90.1% 650 albums, playlist with 10 tracks, probability 6.7% 20 tracks, probability 25.6% 30 tracks, probability 49.3% 40 tracks, probability 70.6% and assuming no replacement (individual tracks do not repeat in the random playlist) 350 albums, playlist with 10 tracks, probability 11.0% 20 tracks, probability 39.3% 30 tracks, probability 68.5% 40 tracks, probability 87.7% 650 albums, playlist with 10 tracks, probability 6.0% 20 tracks, probability 23.4%% 30 tracks, probability 45.8% 40 tracks, probability 68.9% Anyone who is inclined to do their own calculations and has a copy of R (http://www.r-project.org) can use the following code to calculate the "collision probability": collision <- function(albums, playlist, tracks = 10, replacement = TRUE) { n <- albums t <- tracks k <- playlist if (replacement) 1 - exp(lfactorial(n) - lfactorial(n-k) - k*log(n)) else 1 - exp(k*log(t) + lfactorial(n) + lfactorial(n*t-k) - lfactorial(n-k) - lfactorial(n*t)) } Apologies for being a bit of a dag. -- smc2911 ------------------------------------------------------------------------ smc2911's Profile: http://forums.slimdevices.com/member.php?userid=4388 View this thread: http://forums.slimdevices.com/showthread.php?t=19696 _______________________________________________ Discuss mailing list [email protected] http://lists.slimdevices.com/lists/listinfo/discuss
