This has got to be related to the phenomena where odds are good that in a room of 23 people; two of them will share a birthday.
On a given 8 hour drive, I will hear about 75 songs on various radio stations (old classic rock). At least 80% of the time I will hear one song twice during this trip. It seems to me I can make a rough guess of the number of songs in my sphere of listening taste. I don’t know how to do the calculation, and I’m sure my calculator isn’t up to the task. Can someone figure this out for me?.
In any random (not really) group of 75 songs played on radio stations I listen to, there is a 80% chance that one song will be repeated. How many songs are in this universe of songs?
I guess 2000, but its purely a guess. It seems that often the songs are damn obscure so perhaps my universe of music is larger than that.
This is essentially the same as the birthday problem, like you said. In this case, you know that the probability of two people out of 75 sharing a birthday is 80%, and you want to know the number of days in the year, which corresponds to the total number of songs. The formula for calculating this exactly is a bit unwieldy because of the large exponents and factorials involved, but Wikipedia gives a formula to approximate the probability:
p = 1 - exp(n(1-n) / 2d)
where p is probability of two people having the same birthday (80%), n is the number of people (75), and d is the total number of days in the year. Substituting and solving for d gives 1724, which should correspond to the approximate number of songs from which the 75 are chosen. Of course this assumes these songs are all equally likely to be chosen among the 75 listened to, which is probably not the case in real life.
Make sure you take into account if you listen to any “Top 40” stations. From what I was told by someone that works at a KISS station, Top 40 stations are required to play the Top 10 songs every two hours. that means in an 8 hour day, you may hear a specific song up to 5 times if it’s in heavy rotation.
Off topic but I was listening to the radio the other day and heard a song, i switched the station and heard the SAME song in almost the exact same spot, i turned from a station to my AUX for my ipod and the SAME song was playing…thats 3 songs in a row that were all the same
It’s not possible to say because the current song isn’t independent of the last song. If they just played “Sweet Child of Mine”, they’re not going to play it again for a while.