Stop 04 · Statistics for AnalystsTopics · 2/11

Probability Basics

In short

Every A/B test, forecast and risk score is built on probability. You don't need fancy maths, just a few rules and a good feel for randomness.

The foundation for hypothesis testing and A/B testing later — basic rules for combining probabilities, conditional probability, and the intuition behind randomness in data.

The jaadu rolls two dice over a ludo board with coloured tokens.

Think of it like this

Rolling for a six in Ludo

In Ludo you need a six to start. Each roll has a 1 in 6 chance, and the die doesn't remember your last roll. Waiting five turns doesn't make a six 'due'. Probability is just putting numbers on chances like this, honestly.

Watch it happen

Two tosses of a fair coin

Start

H (0.5)

T (0.5)

HH = 0.25

HT = 0.25

TH = 0.25

TT = 0.25

1/4First toss: heads or tails, each with probability 0.5.

The big ideas

What you need to know

Between 0 and 1

0 means impossible, 1 means certain. 0.3 is the same as 30%.

AND: multiply (if independent)

Two independent events both happening: multiply their probabilities.

OR: add (if they can't overlap)

Either of two mutually exclusive events: add them. If they can overlap, subtract the overlap.

Conditional probability

P(A given B) is the chance of A once you know B happened. It's the basis of most real analysis.

Save yourself the pain

Common mistakes

Oops

Believing a result is 'due' after a long streak.

Do this instead

Independent events have no memory. Ten tails in a row doesn't change the next toss.

Oops

Mixing up P(A given B) with P(B given A).

Do this instead

P(cough given flu) is high. P(flu given cough) is much lower. Order matters.

Your mission

Simulate coin tosses

~20 min

Quick check

A fair die is rolled twice. What's the probability of getting six both times?

Go deeper

1Work through a handful of basic probability problems (coin flips, card draws).
2Learn conditional probability with a simple, concrete example.
3Understand why 'random' data can still show short-term patterns that mean nothing.