S3 · Probability · PROB.CONDITIONAL.INTRO

Conditional probability basics

Intuition

Understand first, compress later.

Probability quantifies uncertainty. A good model starts with clear possible outcomes and conditions.

Switch representations

Probability treetwo-stage experiment

branch probabilityhighlighted path (product)outcome with path probability

Along a path the branch probabilities multiply; the result is written at the leaf. Because the situation changes after the first step, the second-stage branches differ — the stages are dependent. The four path probabilities add to 1, because exactly one path must happen.

Formal view

You can conditional probability basics when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.