Online Tool Store
Probability Tree Builder
Add sequential events and their branch probabilities to build a probability tree diagram, with each path's combined probability calculated automatically.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Edit branch labels and probabilities (0–1) for a two-stage tree. Each stage's probabilities should sum to 1 within their branch.
| Path | Joint probability |
|---|
How it works
- Edit the branch labels and probabilities for the first stage (e.g. "Rain" 0.3, "No rain" 0.7) — a worked weather/umbrella example is pre-filled.
- Edit each first-stage branch's conditional second-stage probabilities underneath it.
- The joint probability table and validation check update instantly as you type.
The multiplication rule
P(A and B) = P(A) × P(B | A)
Example: P(Rain) = 0.3 and P(Bring umbrella | Rain) = 0.8 gives a joint probability of 0.3 × 0.8 = 0.24 for the "Rain → Bring umbrella" path. Summing every path's joint probability across the whole tree should equal 1.0.
FAQ
How is the joint probability calculated?
By the multiplication rule for a probability tree: the joint probability of any path is the product of the probabilities along that path — the first-stage branch's probability times the conditional probability of the second-stage branch given the first.
Why does it warn me about probabilities not summing to 1?
A valid probability tree requires each stage's branches (given you're at that node) to be mutually exclusive and exhaustive — meaning something on that stage must happen, so the probabilities from any single node must sum to exactly 1. The warning flags a branch where your entered numbers don't satisfy that, so you can catch a typo before trusting the results.
Can I add more than two stages?
Not in this version — the tool supports two stages (a first branch and a conditional second branch under it), which covers the vast majority of textbook probability tree problems. For a three-stage tree, treat one combined path's outcome as a new "first stage" in a second pass.
How we compare
| Feature | Online Tool Store | Drawing the tree by hand | Spreadsheet formulas |
|---|---|---|---|
| Instant joint-probability table | ✓ | ✗ | ✓ |
| Flags branches that don't sum to 1 | ✓ | ✗ | ✗ |
| Free, no formula-writing required | ✓ | ✓ | ✗ |
A spreadsheet needs you to write the multiplication formulas yourself; this computes every path's joint probability live as you edit branch values, and flags the exact branch if your numbers don't add up.