[ThinkBetter](https://thinkbetter.app/) → [Mental Models](https://thinkbetter.app/mental-models.md) → Bayes' Theorem

# Bayes' Theorem

Probabilities (or the likelihood of something happening) should be updated with new information as we gather it.

![Bayes' Theorem illustration](https://assets.thinkbetter.app/images/bayes_theorem.png)

Bayes' Theorem, named after Reverend Thomas Bayes, who formulated it in the 18th century, is a way to update our belief about something when we gain new information. It's like adjusting your estimate of how likely it is to rain based on the clouds you see in the sky. Mathematically, it relates the probability of an event, based on prior knowledge of conditions that might be related to the event. For instance, if you initially think there's a 30% chance it'll rain today, but then you see dark clouds gathering, Bayes' Theorem can help you update this probability, making it more accurate with the new information. This theorem is more than just a formula; it's a framework for thinking. It tells us that we should adjust our beliefs as we encounter new, relevant information — and that we should weight the relevance of the information in that prediction — rather than sticking rigidly to our first impressions or assumptions.

## Example

**Weather Forecasting**

Updating the probability of rain as the day progresses based on changing weather conditions. Initially, the forecast might say a 30% chance of rain, but if you observe dark clouds forming, you might revise this probability upwards. Why? Bayes' Theorem allows for the adjustment of predictions based on new, relevant evidence, leading to more accurate weather forecasting.

## In your professional life

**Embrace Dynamic Planning**

Regularly update your beliefs about projects or processes as new information becomes available, rather than sticking to initial assumptions. As a project manager in construction, be prepared to adjust your project timeline and resource allocation when unexpected site conditions are discovered. By remaining flexible and promptly communicating changes to stakeholders, you demonstrate adaptability and foresight. This approach not only keeps projects on track but also builds trust with your team and clients, positioning you as a reliable leader in a dynamic industry.

## Go deeper in ThinkBetter

The ThinkBetter app has the full Bayes' Theorem deep-dive: more examples, a quiz to test yourself, audio narration, and a weekly path that builds these ideas into a habit.

- iOS: https://apps.apple.com/app/id6459831884
- Android: https://play.google.com/store/apps/details?id=io.ventureship.braintricks

### Related concepts

- [Probabilistic Thinking](https://thinkbetter.app/mental-models/probabilistic-thinking.md)
- [Base Rate Fallacy (Cognitive bias)](https://thinkbetter.app/cognitive-biases/base-rate-fallacy.md)
- [All cognitive biases](https://thinkbetter.app/cognitive-biases.md)

Page: https://thinkbetter.app/mental-models/bayes-theorem