# Probability

> Random events and likelihood

- Skill: `neuralblitz/probability` (Agent Skill)
- Install (CLI): `npx skillmds@latest add neuralblitz/probability`
- Raw SKILL.md: https://api.skillmd.com/api/skills/neuralblitz/probability/raw
- Safety review: pending (external: skill-scanner PASS, skillspector PASS)
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- License: MIT
- Author: NeuralBlitz (https://skillmd.com/u/neuralblitz)
- Updated: 2026-09-21
- Page: https://skillmd.com/skills/neuralblitz/probability

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## What I do
- Calculate probabilities and conditional probabilities
- Apply Bayes' theorem for inference
- Work with probability distributions (discrete and continuous)
- Calculate expected values and variances
- Apply the central limit theorem
- Use moment generating functions

## When to use me
When analyzing random phenomena, making inferences from data, or modeling uncertainty.

## Key Concepts
- **Probability Axioms**: P(A) ≥ 0, P(S) = 1, P(∪A_i) = ΣP(A_i) for disjoint events
- **Conditional Probability**: P(A|B) = P(A∩B)/P(B)
- **Bayes' Theorem**: P(A|B) = P(B|A)P(A)/P(B)
- **Expected Value**: E[X] = Σ x·P(X=x) or ∫x·f(x)dx
- **Variance**: Var(X) = E[X²] - (E[X])²
- **Central Limit Theorem**: Sum of i.i.d. variables approaches normal distribution