Possibility or Probability?
“Sometimes people say to me Pastor Jeff, how do you know there is a God?”
“And I say it’s simple math God either exists or he doesn’t.”
“So, let’s be cynical worst-case scenario there’s a 50/50 chance and I like those odds.”
You may heard these famous phrases in Young Sheldon series that the Pastor Jeff makes a point to the people that the God exists using simple yet subtle physics theory.
In the series Sheldon tries to point out the difference between the “Possibility” and “Probability” by using an interesting example,
“You’ve confused possibilities with probabilities. According to your analogy (Pastor’s) when I go home I might find a million dollars on my bed or I might not. In what universe is that is 50/50?”
yet failed.
So, have you ever wonder what that Sheldon meant? What is Possibility and what is Probability, what is the difference, is there a difference at all?
That’s the kind of questions raised inside my head when I heard those phrase. Out of curiosity I searched for the difference between these two and have a clear idea. Through this I brings you the subtle yet one of the important distinction that often gets blurred in everyday and some philosophical questions to think about.
What is “Possibility”?…………….
In Science, Possibility refers to whether something can happen at all, it’s about logical or physical feasibility. For an example,
“It’s possible to roll a six on a die.”
This doesn’t tell us how likely it is, only that it’s whithin the realm of outcomes. In simple it is 0 or 1 at a given time, or “True” or “False”.
Then what is “Probability”?……………
It refers to how likely that possible event is to occur, usually expressed as a number between 0 and 1 (or 0%-100%). For an example,
“The probability of rolling a six on a fair die is 1/6 ≈ 16.7%”
This quantifies the chance of the possible event happening.
In Young Sheldon, he was highlighting that saying “Something is possible” is not the same as saying “it is probable”. For example,
It’s possible the Earth could be hit by a giant asteroid tomorrow. But the probability is astronomically low according to the facts and data at the present. As continue thinking about this you may come to a point that thinking,
“So in theoretically there can be a possibility of happening anything, hence there should be a probability also (Maybe a tiny that is insignificant) right?”
You got the right intuition, but there is a subtle catch here.
Here’s a continuation that picks up right where you left off and keeps your voice:
The Catch: Possible Doesn’t Always Mean “Has a Probability Greater Than Zero”……………
Mathematics has a surprise here. An event can be possible and still have a probability of exactly zero.
Imagine throwing a dart at a dartboard. Assume the dart is infinitely sharp and lands on a single point. What is the probability that it lands on one exact point, say the dead center of the bullseye, down to the last atom and beyond?
Now count the points on the board. There are infinitely many. If every point had even a tiny probability, the total would add up to infinity. But total probability can never be more than 1 (100%). So each individual point must have a probability of 0.
The dart still has to land somewhere. Wherever it lands, that point had probability 0, and it happened anyway. So it was clearly possible.
Mathematicians have a name for this: an event with probability 1 happens “almost surely”, and an event with probability 0 happens “almost never”. This is different from “impossible”. Landing on the center point is almost never. Landing on the wall behind you when you aimed perfectly is a different story.
So the more accurate picture is:
- Impossible → probability 0 (always true)
- Probability 0 → impossible (NOT always true!)
Your intuition was close. In everyday, finite situations like dice, cards, and coins, anything possible does get some probability above zero. But once infinity enters the picture, “possible” and “probable” separate even further than Sheldon suggested.
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The Second Catch: Probability Needs a Model……………
There’s an even deeper point. To give something a probability, you need more than a list of outcomes. You need a model: some reason, data, or structure that tells you how much weight each outcome deserves.
For a fair die, the model comes from symmetry. Six identical faces give no reason to prefer any one, so each gets 1/6.
For the asteroid, the model comes from astronomy: observations, orbital calculations, and impact records.
Without a model, you can say something is possible, but you can’t honestly put a number on it. You can say “it’s possible” about almost anything. “It’s probable” is something you have to earn.
So, Where Did Pastor Jeff Go Wrong?……………
Pastor Jeff’s reasoning looked like this:
There are two outcomes → so each is 50%.
This is the mistake Sheldon pointed out. Counting outcomes is not the same as weighing them. Two outcomes only get 50/50 when you have a good reason to think they’re equally likely, like the two sides of a fair coin.
Look at some other “two outcome” situations:
- You either win the lottery tomorrow or you don’t. 50/50?
- A random person you pass on the street is either your long-lost twin or not. 50/50?
- You go home and find a million dollars on your bed, or you don’t. (Sheldon’s example.) 50/50?
Each has exactly two outcomes, and none of them is anywhere near 50/50. The number of outcomes tells you nothing about the odds by itself.
To be fair to Pastor Jeff, this isn’t a verdict on whether God exists. That’s a question people have debated with far more careful arguments for thousands of years, and they still disagree. The point is only that this particular argument doesn’t work. “Either it is or it isn’t” is true for every yes-or-no question, so it can’t tell you the odds of any of them.
Why Does This Matter Outside Young Sheldon?……………
This confusion shows up everywhere once you notice it:
- Fear and anxiety: “It’s possible the plane crashes” is true, but the probability is tiny, far lower than the risk of the drive to the airport.
- Conspiracy thinking: “It’s possible that…” is often used as if it proved something is likely.
- Scams and gambling: “You could be the next big winner!” says nothing about your actual chances.
- Software and engineering (my own field): a bug that’s possible but has a one-in-a-billion chance per request might still happen many times a day on a system handling billions of requests. Here the probability matters more than the possibility.
Asking “Is it possible?” is only the first step. The better question is “How likely is it, and how do we know?”
Some Questions to Think About……………
Here are a few questions that stuck with me. I don’t have final answers to all of them:
- If an event has probability exactly 0 but still happens (like the dart), what does “probability” really mean? Is it describing the world, or describing our knowledge of it?
- When we have no data at all, is it ever reasonable to assume outcomes are equally likely? Or is that just Pastor Jeff’s mistake dressed up in nicer clothes?
- Can a probability be wrong? If a weather app says 90% rain and it stays sunny, was the app wrong, or did the 10% just happen?
- Are there questions that simply don’t have a probability, where the most honest answer is “it’s possible, and that’s all we can say”?
Final Thoughts……………
Sheldon was right, even if he couldn’t convince anyone in the room. Possibility asks can it happen? It’s a yes or no. Probability asks how likely is it? It’s a number, and you have to earn it with reasoning or evidence.
The subtle catch goes further than Sheldon said. Something can be possible and still have zero probability. And without a proper model, some things can’t be given a probability at all.
So next time someone tells you “it’s 50/50, it either happens or it doesn’t,” you’ll know what to say. And unlike Sheldon, maybe you’ll even convince them.
