Misunderstanding Probability

On Christmas eve, I had a fun conversation with a rocket scientist and a lawyer about probabilities. No, this isn't the opening line of a corny joke. We talked about love and the chances that the lawyer would have ended up with his lovely wife of many years. He concluded that if you chain the probabilities, it was a Christmas miracle that they ended up falling in love. And we methodically went through the historical series of chance events and unlikely scenarios that occurred many years ago for these two love birds to end up together. The Rocket Scientist concurred - yes, indeed, the probability is one tick above 0.0.

Though a beautiful story, that's not how probability works. I hate to be Scrooge here, but we can't calculate some ex-ante probability from ex-post information. The infinitesimally small probability assigned to the story's outcome only makes sense if calculated before they meet!

To make an analogy, suppose I was to take a walk along a sandy beach. The beach goes for miles in each direction. I carelessly stroll along for a while and then, on a whim, pick up a handful of sand, letting all of the grains fall through my fingers, except for one. I then claim, "Wow, what are the chances that I would have picked up this grain of sand? There are billions upon billions of grains of sand on this beach. Imagine the odds!" Using the same flawed logic previously mentioned, the rocket scientist and the lawyer would have to claim, "one in several billion!"

But yet, no matter what grain of sand I chose, I could claim to be astonished and call out, "Imagine the odds!". A thousand times in a row I could walk the beach, pick up a grain of sand and be amazed at the unlikeliness of yet another one-in-several-billion event coming true.

Now, if someone chose a grain of sand ahead of time, and I somehow picked that exact grain of sand, well, that would change everything and would be a bonafide Christmas miracle. Order matters - ex-ante and ex-post make all the difference.

We can also invoke Bayes' Thereom here. Bayes describes that once there is new information - that they met and fell in love - the probability of the outcome changes. P(A|B) is not P(A). So as Scrooge-like as it may be, the probability that a couple fell in love - given that they fell in love - is not 0, but instead 100%.

Ok, I'll shut up now. Nobody in their right mind should be invoking Bayes' Thereom on Christmas Eve. I'm all for calling it a Christmas miracle.