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View Full Version : Stupid probability question

11-30-2002, 06:36 PM
The other day, while in the car, I heard the songs "goodbye to you" and "Drops of Jupiter" back to back. A couple of days later, I heard those two songs back to back *again*! Wow! What are the odds of hearing those two exact songs back to back twice in a couple of days?! And don't give me any garbage about how there were a lot of other songs that could have been played back to back, and weren't, so I didn't notice. I'm only interested in the probability of hearing those two exact songs back to back twice!!!
All right, this is meaningless and I'm being an idiot, but I read stuff like this on this forum all the time, and it makes about as much sense.

David Ottosen
12-01-2002, 08:07 PM
Let's assume that this was a poppy type station that plays about 40 different songs. So, you have a 1/40 chance of hearing one of these songs. Then you have a 1/39 chance of hearing the next song. So about 1600-1 against hearing these two songs back to back as the NEXT two songs you hear. Then another 1600-1 against hearing them back to back again, assuming fair distribution of playlist. So 1-25600 or so? And think...rather than use this incredible statistical devation to win the lottery...you used it to listen to the radio. Woops.

MSchmahl
12-01-2002, 11:58 PM
I will assume, as you do, that each song has a 1/40 chance of being played. Let's also assume that you listen to about 10 songs per day. The probability of hearing "Goodbye to you" in the first nine songs is 9/40. The probability that the next song is "Drops of Jupiter" is 1/39.

So the probability of hearing these two songs back-to-back in that order in a given day is 0.58%. The probability that this would happen on two particular days is 0.0033%. The question specified "a couple of days later". The probability of hearing these two songs, back-to-back twice within a particular 3-day period is about three times that, or 0.010%, which is 10,000-to-1.

If the question were "What are the odds of hearing these two exact songs consecutively, in order, in a 3-day period sometime this year?", the answer would be about 30-1 against.

If the question were "What are the chances of hearing any two songs, consecutively, in the same order, twice in a specific 3-day period?", the answer would be about 15%, only 5.6-1 against.

If the question were "What are the chances of hearing any two songs, consecutively, in order, twice, only a couple of days apart, sometime this month?", the answer would be about 95.5%, which is 21.7-to-1 on.