A few weeks ago I had a really interesting conversation about probability with my friend Scott. I was jokingly telling him that I think the probability of everything is 50/50. In a bag of 10 different colored marbles, the probably of picking blue is 50% because you either pick blue or you don’t. Things either happen or they don’t! This obviously isn’t the way that probability actually works, but Scott brought up his own interesting theory that I’ve been thinking about a lot lately.
Scott’s argument begins with the fact that probability is purely a posteriori, meaning that we are only able to determine probability after measuring observed outcomes. Because of this, outcomes are not in fact determined by probability. Things happen exactly as they are meant to, and probability is just an observed pattern based on similar recurring events. Scott pointed to the improbable existence of humanity as a perfect example of a deterministic fate (God’s will) rather than a happenstance of chance.
The main hole that I tried to poke in Scott’s argument was that if I was to assign 6 different life choices to 6 sides of a die, I could use the outcome of the die to determine God’s will in my life. Scott’s counter was that his theory only applies to probabilities that are assigned to things with meaning. Although his notion of “meaning” seemed to be kind of general and subjective, I still thought it was an interesting idea.
There was a prominent Italian statistician named Bruno de Finetti who provocatively stated that “probability does not exist”. His argument was that probability does not exist objectively but instead only exists subjectively within the minds of individuals. In many ways, he was essentially saying that probability is a personal measure of the risks we are willing to take. This risk in fact has nothing to do with actual outcome.
I always find it fascinating to think about the improbable circumstances that have led to my life as it is today. The chance that my mom and dad fell in love, the chance that I have the friends I do, the chance that I live in the place I live with the job I have. I simply can’t bring myself to believe that all of these things were subject to simple probability. Yet at the same time, there is a dark side to probability as well. When you think about the question of why bad things happen to good people, sometimes it’s easier to believe in probability than God.
There’s obviously a lot more to unpack here, but I do want to conclude with one thought. There’s a famous Wayne Gretzky quote that says “You miss 100% of the shots you don’t take”. Even though it’s one of those quotes that has become cliche, I still think it highlights something incredibly important about probability. Whether the outcomes of our decisions are willed or subject to chance, we are still left with the freedom of choice. Sure it might seem highly improbable to land a dream job or find a soulmate, but the a priori and a posteriori probability both become zero if you choose not to take a risk at all. So maybe I was right about probability … either you take a chance or you don’t!