Statistics · Probability
Chapter 1 · 4
The idea
Conditional probability and tree diagrams
Using tree diagrams where the second-stage branches are conditional probabilities — multiplying along branches for P(A ∩ B), adding the paths to an event, and reversing the condition to find P(first | second).
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Statistics · Probability
Conditional probability and tree diagrams
Using tree diagrams where the second-stage branches are conditional probabilities — multiplying along branches for P(A ∩ B), adding the paths to an event, and reversing the condition to find P(first | second).
Why it works
A tree IS the multiplication formula
A tree diagram is really a picture of the multiplication formula. The first set of branches shows the first event; the second set, growing from each, shows the next event given the first — so the second-stage probabilities are conditional. That is why you multiply along a path: is exactly the two probabilities on the branches multiplied together.Where it bites: dependent stages
This matters most when the stages are dependent — above all "without replacement", where taking the first item changes the probabilities for the second. Drawing two counters from a bag of red and blue: the first branch is red, but the second branch given red is — only counters are left and one red is gone. The conditional probabilities live on the second branches.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
Start freeTakes a minute — no card.