(Submitted by reader Alex Murdoch)

I got home from work today and was getting ready to cook a stir fry for dinner for the family. There was lots of noise, so I decided to put on my MP3 player and catch up on some podcasts.

Turns out I was all caught up, so I switched over to music and put my player on shuffle. A few song later I was feeling pretty good and singing along at a good volume. The song I was belting out was “Too Much Time on My Hands” by Styx.

My wife comes in and taps me on the shoulder. I took my right earbud out and she says:”What are the odds of that?” She pointed to her tablet where she was listening to Slacker Radio: Classic Rock. You can probably guess what was playing…yup. Styx: Too Much Time on My Hands.

I’ve got just over 800 songs on my player. So…help me answer my wife: What are the odds of that?

Below are the extended notes provided by Ed Clint for use in Skepticality Episode 213.  Take a look and leave your comments below. Also, please be sure to listen to the podcast for our own sarcastic and hilarious commentary.

Ironically, almost everyone can remember a version of this sort of “million to one” experience. Such as when someone picks up their phone to call someone only to have it ring by way of said someone or hearing your name called out in a waiting room to find out a second person with yours or a very similar name is also waiting. I once found a comment left on the Reddit social news website left by my brother. It was just one comment out of tens of thousands or hundreds of thousands posted that day to hundreds of discussions, most of which I never look at, and of the ones that I do, I could only see a fraction of the individual comments. The operant psychological mechanism is a form of confirmation bias, the attributing of meaning to events that merely coincide. After all, how many times does anyone note failures of coincidence in their life? How do we even guess at the number of failed coincidences? How could we check? What are the odds?

One music player had 800 songs and the other was playing from a “classic rock” mix. We can’t be sure how many tracks were in rotation in the mix, or which were favored because that depends on the listener’s previous choices. For the sake of argument, let’s conservatively estimate the Styx track was one of 1200 that might be in regular rotation. This would meant that at any one time both people were listening to music (assuming the Slacker Radio listener had selected “Classic Rock”), the odds are 1 in just under a million. If the Slacker Radio listener only likes “Classic Rock” occasionally, let’s say just 1/5 of the time she listens to music, the odds become closer to one in 5 million.

That sounds pretty unlikely, until you consider that none of the details have been specified in advance. In statistics, probability is the chance of a given outcome divided by the number of possible outcomes. So we can say the chance of a flipped coin landing on heads is .5 because there are two possible outcomes and heads is one of them. In our musical example: how can we decide what the meaning of “given outcome” or “possible outcomes” is? It’s cheating to decide after the fact, because the odds of any two songs playing simultaneously are equal to the odds of the same song playing on both sources. Instead, it is our intuitive psychology that defines what is meant by “unlikely hit” which casts the roles for expected and given outcomes.

Humans are pattern-seeking critters because nature rewards the pattern seekers: weather, climate, animal migration, and the co-location of flowers and bees with fruits and honey are all that dots it pays Darwinian dividends to be able to connect. The pattern sense necessarily registers false positives, connecting irrelevant dots. Now we can define the terms more clearly: the “given outcome” is any event that a person might experience that triggers the pattern recognizer and the “possible outcomes” are the set of events a person might experience which might trigger the pattern recognizer, but happens not to.

On the day the same songs played, the two people might have ordered the same improbable lunch, been humming the same theme to a beloved 80’s TV show, or stumbled on the same obscure internet article. If these events coincided, they’d each trigger the “what are the odds?” pattern recognizer sense. How many other potential “one in 5 million”-ish events might have happened but didn’t? This is difficult to guess, but I suspect hundreds or more, multiplied by any two people that may interact. When multiplied by 365 days, the odds get decidedly saner.

For the sake of argument, let’s restrict our consideration to musical coincidence. One in five million is steep, but then we only heard from this person and not one of the other 115 million households in the US (assuming this person is American). If our rough estimate is correct, the odds are that 23 other pairs of people have the same experience on days they feel like playing some tunes.

Edward Clint co-created the Skeptic Ink Network with John Loftus and writes about Evolutionary Psychology, critical thinking and more at his blog Incredulous. He is presently an intern at the JREF and a bioanthropology graduate student at UCLA studying evolutionary psychology.

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