S2 · Probability · PROB.TREE

Probability trees and multi-stage probability

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 probability trees and multi-stage probability 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.