The Probability Problem

“Probability fractions arise from our knowledge and from our ignorance.”


Probabilities are everywhere. The weather, business forecasts, sports results, elections, and even personal choices.

They also play a vital part in the basic layer of reality through quantum mechanics (no shit).

This means our world is naturally based on probabilities; nothing is guaranteed and many things are possible.

Yet, we often get them wrong and make poor choices because of it.

Why? Because there’s something strange about probabilities almost no one ever talks about: there are different kinds and they almost have nothing to do with one another.

We can view probabilities through the lenses of math, statistics, physics, economics, or philosophy.

And whatever we do, three main differences remain:

  1. Probabilities based on objective facts about the world
    1. The probability of rolling a three with a 6-sided die
    2. The probability of flipping heads with a 2-sided coin
    3. The probability of pulling the Queen of Spades from a deck with 52 cards
    4. ...
    5. In these situations, there are existing real-life characteristics. If we know everything about these characteristics (like knowing that the die is fair and has six sides), we can calculate a definite probability.

  2. Probabilities based on objective historic events
    1. The probability of the stock market gaining more than 10% in any given year
    2. The probability of a tech startup surviving its first five years
    3. The probability of Bayern Munich winning the German Bundesliga in any given year
    4. ...
    5. In these situations, there aren't any present real world features, but trustworthy historic real world frequency data that we can use as a substitute for chances.

      Remember, in these situations, you can't calculate a definite current probability, but you can make educated guesses based on the past. Plus, the more information you have about the current situation (like the economy's condition or the sports team's performance), the better you can adjust your probability estimates.

  3. “Probabilities” based on subjective assumptions and personal beliefs
    1. The probability of you making a good career at a particular company
    2. The probability of a business strategy yielding a profit
    3. The probability of a specific political situation leading to war
    4. ...
    5. In these situations, we don't have any present real-life characteristics, or trustworthy past real-life data to use as a substitute. Instead, we form opinions based on what we see, personal experiences, assumptions, and personal beliefs.

      Here, more information about the environment's condition will also lead to changed assumptions, thus producing different probability estimates.

Understanding probabilities is simple in the first case. But in the second and third cases, it's not as clear. Using the term "probability" might make us think we know more about reality than we actually do.

While in maths and statistics, probability science quickly becomes highly complex, nuanced and often counter-intuitive, philosophy and the foundations of physics debate whether probabilities truly exist at all at a fundamental level — or if they always just point to our lack of information in different contexts.

Even though probabilities can be difficult to grasp, understanding the differences between the three examples above can help us make smarter choices when things are uncertain and protect us from making incorrect predictions.

“Probability fractions arise from our knowledge and from our ignorance.”

— Ian Hacking

Here are 3 other concepts you might benefit from: