So I carry a thumb drive with me, and play music from a library of a couple thousand songs eight hours a day at work. I don't bother pausing when I get up for break/lunch/meetings, I just mute my headphones. When I start playing music in the morning, it begins exactly where it was when I closed the music player the previous day. In effect, I have created an infinitely looping playlist of a few thousand songs. Most of these songs are the typical 3-4 minutes, while some are video game OST's that can be 4-5 hours long.
I've been wondering, assuming the "random" feature on my media play is truly random how should I calculate the odds of catching a specific song at any given time if I put my headphones in? The randomization does not require all songs to play in the set before it will replay any, it can (and has) played the same song multiple times in a row. I'm thinking that based on the ratio of "long" tracks to regular length tracks, it should lean heavily towards me putting on my headphones during a short song, but it really seems to be about 50/50 of catching a "long" track.
Here's an example data set similar to what I'm trying to calculate on. Obviously, this group would be VERY likely for me to pick it up on a "long" song, but It'd be great to see how the probabilities could be calculated from it.
AC/DC - Back in Black 4:10 AC/DC - Shook me all Night 3:31 The Beatles - Come Together 2:04 Daft Punk - Contact 4:27 FF9 Full OST 325:35