Probability & Statistics Mind Map

Every probability & statistics visualization on this site on one map. The branches are the main ideas. Each leaf is a page; the grey line under it is the one thing to remember about it. Click a branch to focus on it, click a page to open it.

Recall mode hides the page names. Read the hint, say the name, then click the "?" to check.

1. How the map is organized

Overview of the probability & statistics mind map: Counting, Conditional probability, Distributions, Random processes, Statistics from data. — The map at a glance: 5 branches, 18 pages.

Ask which way the question goes:

From a known model to chances? That is probability: counting when outcomes are equally likely, distributions for whole sets of values, conditional probability when new information arrives.
Too hard to compute exactly? Simulate it many times: random processes.
From data back to the model? That is statistics: summarize, estimate a range, or test a claim.

2. The branches side by side

Branch	Question	Key formula
Counting	how many ways?	C(n,k) = n! / (k!(n−k)!)
Conditional probability	how likely, given what I know?	P(A\|B) = P(B\|A)·P(A) / P(B)
Distributions	how likely is each value?	N(μ, σ²), Poisson(λ)
Random processes	what happens over many runs?	error ~ 1/√n; πP = π
Statistics from data	what does the sample say?	standard error σ/√n

3. Five facts to remember

Always use the base rate: with a rare disease, most positive tests are false positives.
The average of n draws has spread σ/√n: four times the data halves the error.
The central limit theorem makes sums and averages normal, whatever the starting shape.
A p-value is P(data at least this extreme | H₀), not the probability that H₀ is true.
A 95% confidence interval means the method catches the true value in 95% of repeated samples.

See all probability & statistics pages in the index, or the other mind maps.