# Probability & Statistics

Almost every important decision is made without certainty - will this launch work, is this result real,
is that headline's scary number actually scary? **Probability** is the math of *how likely*, and
**statistics** is the math of *making sense of data* once you have it. They are the two halves of
thinking clearly about an uncertain world, and they're the last foundation in the Mathematics track for
a reason: nearly everything downstream - A/B tests, machine learning, risk, polls - runs on them.

There's a second reason this guide matters more than most. Numbers are the favorite costume of
misleading arguments: a cherry-picked average, a biased sample, a chart with a doctored axis, a
"correlation" sold as a cause. The same statistics that help you understand the world are the ones used
to bamboozle you about it. So this guide does both jobs - it teaches the tools straight, and it teaches
you how those tools get *abused*, so the next misleading number doesn't get past you.

## How to read this
- **Want the core idea?** [Phase 1](01-probability-measuring-uncertainty.md) is probability from zero.
- **Want the self-defense?** [Phase 3](03-how-statistics-mislead-you.md) is the catalog of how numbers
  lie - but Phases 1–2 are what let you spot it.

## The phases
1. **[Probability: Measuring Uncertainty](01-probability-measuring-uncertainty.md)** - likelihood from 0
   to 1, combining events, and expected value.
2. **[Reading Data: Statistics That Don't Lie](02-reading-data-statistics.md)** - mean, median, spread,
   and the shape of a distribution (and when the mean betrays you).
3. **[How Statistics Mislead You](03-how-statistics-mislead-you.md)** - correlation vs causation,
   sampling bias, base rates, and the charts built to deceive.

> This builds on [Counting & Combinatorics](/guides/counting-and-combinatorics) (probability is counting
> favorable outcomes) and pairs with
> [Critical Thinking & Fallacies](/guides/critical-thinking-and-fallacies). It's the final guide of the
> Mathematics foundations.