The probability of a 'hit' song in your head playing on the radio when you get in your car

On my way to hockey this morning (6:45am), Sufjan Stevens (hopefully I just butchered his name) was playing on the current. It just happened to be the song that was stuck in my head, since they played it on the radio the day before (at least the female backing harmony chorus part was stuck in my head). Btw, the song is from Age of Adz, but I haven’t the foggiest about the name. On to math…

What is the probability that a song that is playing in your head will be on the radio when you turn on your car?

The variables:

Time of Day
Radio Daily Playlist
Song length
Number of times you enter yourcar through out the day

I’m probably missing some, but let’s start breaking it down.

While true that there are 24 hours in a day, let’s ignore most of those, since a radio station is going to focus its ‘hits’ on the hours when people will actually be listening. Let’s say 6am - 8pm? Roughly 14 hours. Maybe I’m being a little generous, but let’s run with it.

Now, there is only one song in my head, and we’ll assume it gets played every day, since it’s a ‘hit’ song. We’ll consider the average length of a radio song on the current is 4 minutes (they do play longer tracks and this will make math easier). We’ll also assume maybe 12 minutes per hour of the DJs talking or advertising (it’s probably a lot more).

14 hours * 60 minutes = 840 minutes of prime radio time
14 hours * 12 minutes = 168 minutes of no music
840 - 168 = 672 minutes
672 total minutes of prime music / 4 minutes of song length = 168 songs played through out the day (the song in our head is one of those)
0.05% of the song being on the radio

Now, I enter my car (remember going to and from places); 2x hockey, 2x work, 2x lunch, 2x soccer, 2x errand… About 10 times a day.

0.06% * 10 = 0.6% chance that a ‘hit’ song that is in my head will be on the radio when I enter my car…

In terms of days… About every 167 days, a ‘hit’ song that is in my head will be playing on the radio when I turn on the key to my car… Which, in the grand scheme of things is not bad at all…

Obviously, the math above is rough, but it was one of those moments where someone less inclined to understand probabilities would shout, “OMG, there is some magic force that knew that I wanted to hear that song and played it on the radio just for me!” When in actuality, it is probably a decently frequent (in the grander scheme of things) occurrence. I’m sure if you took a more commercial radio station that repeats ‘hits’ constantly the number jumps way up.

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