Re: Stupid probability question
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.
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