# Sharpen Your Mind,

Simplify Your Choices

Join the **Re:Mind Newsletter:** Your Biweekly Guide to Clearer Thinking and Smarter Decisions

## Bayes’ Theorem

By Juan Carlos

# Definition

A mathematical formula to evaluate anything in probabilities based on all the available data, rather than one’s own biases.

# Why Use It

Say someone in a family argues their chain-smoking grandfather, who lived to see 100 years old, is proof that smoking doesn’t kill. That ignores decades of data to the contrary and is by no means the norm.

By integrating probabilistic thinking into your life, you can rely less on hunches and feelings that can impede seeing reality. It’s a remedy to “I know a man syndrome,” where folks overvalue a story and use it in place of statistical analysis.

# When to Use It

The key to Bayesian thinking is your capacity to attach probabilities of accuracy to something you believe to be true. Then, as you receive new data, to update those probabilities and change your mind where necessary.

Folks often welcome or refuse new information without reflection, whereas a Bayesian would consider new evidence against their original conclusion.

Asking yourself questions like, “How confident am I in this position?” and “What kind of data would make me reconsider it?” is key to seeing issues openly.

# How to Use It

Recognize your beliefs are not black and white; instead, they are grayscale with degrees of certainty. As such, your assumptions are on a range greater than zero and less than one hundred percent, enabling you to hold less firmly to views, accept new information, and let those views fluctuate. Don’t lose sight of the bigger picture when new data becomes available.

# How to Misuse It

Even though something has a high probability of being right doesn’t make it so.

For example, a farmer feeds their chickens every day; by that relationship, a chicken might come to believe the farmer is looking out for them. Based on the evidence, the chicken assumes they’ll be fed in perpetuity instead of slaughtered, but one day they find out the reverse is true.

Bayesian thinking is an approach to better understanding, not a solution for perfect judgment.

# Next Step

Use uncertainty to your advantage, rather than seeing it as a weakness. According to Charlie Munger, “If you don’t get this elementary, but mildly unnatural, mathematics of probability into your repertoire, then you go through a long life like a one-legged man in an ass-kicking contest. You’re giving a huge advantage to everybody else.”

Dive a bit deeper into the theorem and equation to update your assumptions: Given a hypothesis (*H*) and evidence (*E*), Bayes’ theorem states that the relationship between the probability of the hypothesis before getting the evidence *P*(*H*)and the probability of the hypothesis after getting the evidence *P*(*H*∣*E*)is *P*(*H*∣*E*)=*P*(*E*)*P*(*E*∣*H*)*P*(*H*).

Take the time necessary to learn and understand it because Bayes’ Theorem has a high probability of changing your life.

# Where it Came From

The seed of Thomas Bayes’ theorem was in his famous work, “An Essay toward Solving a Problem in the Doctrine of Chances,” and went unnoticed until two years after his death when his friend, Richard Price, brought it to the Royal Society’s attention in 1763. Other scholars, such as Pierre-Simon Laplace, developed and cemented the theorem into what it is today.

## 50 Essential Mental Models

## Cookbooks

## Hi, I’m

Juan Carlos

I’m a creator at heart, a filmmaker by instinct, and a polymath who thrives on diversity. My life’s work is about framing: capturing, exploring, and sometimes breaking conventional boundaries to uncover deeper truths.

## My Story

From directing award-winning films to leading product innovation at startups, my career spans the creative and the analytical. I’ve authored children’s books under desert skies, each designed to spark curiosity and independent thought in young minds. Whether through technology that simplifies complex issues or through mental models that enhance clarity, I constantly strive to reimagine how we perceive and interact with the world.

In my personal life, I’m a father fascinated by nature and humanity’s marvels. I share this wonder with my children as we explore the world’s beauty together. Every day offers a new frame, reminding us that what we focus on defines our lives’ story.