treediagrammaker.com

Probability Tree Diagram Maker

Put each branch's probability in (parentheses) and the tree multiplies along every path, shows P at each leaf, and warns you when branches don't sum to 1. Free, no signup.

Outline

Indent = child (Tab or 2 spaces) · (0.5) probability · [yes] branch label

0.50.50.50.50.50.5HeadsTailsHeadsHeadsTailsTailsStartP = 0.25P = 0.25P = 0.25P = 0.25

The two rules of probability trees

Every probability tree question comes down to two moves. Multiply along a path when you need this and then that to happen: the path's probability is the product of its branch probabilities. Add between paths when several distinct paths all count as the event you care about. And at every branch point, the probabilities leaving a node must sum to 1 — something has to happen.

The preset above shows two flips of a fair coin: each branch is (0.5), so every complete path works out to 0.5 × 0.5 = 0.25. The probability of getting exactly one head is the sum of the two paths that qualify, HT and TH: 0.25 + 0.25 = 0.5.

Worked example: marbles without replacement

A bag holds 3 red and 2 blue marbles. You draw one, keep it out, and draw again. Paste this into the editor (or load it from the examples):

Start
  (3/5) Red
    (2/4) Red
    (2/4) Blue
  (2/5) Blue
    (3/4) Red
    (1/4) Blue

The first draw is red with probability 3/5. If it was red, only 2 red remain among 4 marbles, so the second draw is red with probability 2/4. The four paths come out as:

The four leaves sum to 0.3 + 0.3 + 0.3 + 0.1 = 1 — a built-in sanity check for any tree you draw. From here questions become additions: P(both marbles the same color) = 0.3 + 0.1 = 0.4. P(at least one blue) = 1 − P(red, red) = 1 − 0.3 = 0.7.

Why draw the tree at all?

Because conditional probability is where intuition quietly fails. The tree makes the conditioning visible: the second-draw branches literally hang off the first-draw outcome, so "2 of the remaining 4" is impossible to miss. Teachers ask for trees in exams for the same reason this tool checks your branch sums — the picture catches the errors the algebra hides. When your working needs to end up in a document, export a clean PNG or PDF, or copy the plain-text version straight into your notes.

Frequently asked questions

Do I multiply or add probabilities in a tree diagram?

Multiply along a path (this AND then that happening), and add between whole paths (this path OR that path leading to the event you care about). This tool multiplies along each path for you and shows the result at every leaf.

What should the branches from one node add up to?

Exactly 1 (or 100%), because the branches cover every possible outcome of that step. The tool checks each set of sibling branches and shows a warning when they don't sum to 1.

Can I enter probabilities as fractions or percentages?

Yes — (0.5), (50%), and (1/2) all work. Fractions are often the clearest choice for without-replacement problems like drawing marbles, where denominators shrink at each step.