Probability Tree Diagram Maker
Type the branches of a probability tree — or draw items from a bag with or without replacement — and get the diagram with every branch probability, the probability of each outcome multiplied out, and a tick-box event that adds outcomes together. Probabilities are exact fractions, checked to add to 1 at every split, and the diagram downloads as SVG or PNG. Runs in your browser — nothing is uploaded. Free, no sign-up.
Write each branch as a label and its probability: 0.3, 30% or 3/10. Leave one probability off in a group and it is worked out as the rest. If a label ends in a number, put a colon after it (Roll 1:).
Outcomes and the addition rule
| In the event | Outcome | Multiply along the branches | Probability |
|---|---|---|---|
| Rain, Late | 0.3 × 0.6 | 0.18 | |
| Rain, On time | 0.3 × 0.4 | 0.12 | |
| Dry, Late | 0.7 × 0.2 | 0.14 | |
| Dry, On time | 0.7 × 0.8 | 0.56 |
Probability of the ticked outcomes: 0.18 + 0.14 = 0.32 (8/25)
All 4 outcomes together add to 1, as they must.
Title and figure style
Takes the title out of the image and sets the figure number in bold and the title in italics above it — the APA 7 layout.
How to Use the Probability Tree Diagram Maker
- 1. Choose how to define the tree. Type the branches yourself for conditional probabilities (a weather forecast, a medical test); repeat one stage for independent events (coin tosses, dice); or describe a bag of items and let the draws build the tree.
- 2. Enter the branches. One per line with its probability — 0.3, 30% or 3/10 — indented under the branch it follows. Leave one probability blank in a group and it becomes whatever is left.
- 3. Read the diagram and the table. Each branch shows its probability; each path ends in an outcome whose probability is the product along the path. Tick outcomes to build an event and see their sum.
- 4. Download the picture. SVG for a document or slide, PNG for anything else; the APA option moves the figure number and title above the image.
The Two Rules a Tree Diagram Shows
A probability tree turns two rules into drawing. The multiplication rule: the probability of a path is the product of the probabilities along its branches, because each branch after the first is a conditional probability — the chance of that outcome given everything before it. The addition rule: the probability of an event that can happen along several paths is the sum of those paths' probabilities, because the outcomes are mutually exclusive.
- Branches from one node add to 1. Every possible result at that point appears exactly once. The maker checks this exactly (0.3 + 0.7 is 1; 0.33 + 0.33 + 0.33 is not) and names the group that fails.
- Independent stages repeat the same numbers. After a coin toss the next toss still has 0.5 on each branch.
- Dependent stages change them. Drawing without replacement alters what is left, so the second-stage branches differ by what was drawn first. The bag mode works those out from the counts.
Worked Example: Rain and Being Late
The default tree says it rains with probability 0.3. If it rains you are late with probability 0.6; if it is dry, with probability 0.2. The path Rain, Late has probability 0.3 × 0.6 = 0.18, and Dry, Late has 0.7 × 0.2 = 0.14. Ticking both gives the probability of being late whatever the weather: 0.18 + 0.14 = 0.32, which the maker also shows as the fraction 8/25.
Trees also set up Bayes' theorem. Given that you were late, how likely was rain? That is the Rain, Late outcome as a share of all the late outcomes: 0.18 / 0.32 = 0.5625, not the 0.3 you started with.
Drawing from a bag
Take a bag with 5 red and 3 blue items and draw two without putting the first back. The first draw is red with probability 5/8; the second then has only 7 items left, so red is 4/7. P(red, red) = 5/8 × 4/7 = 5/14 = 0.3571. The probability of at least one red is 1 − P(blue, blue) = 1 − 3/28 = 25/28 = 0.8929. If you replace the item each time, the second-stage probabilities stay 5/8 and 3/8, and P(red, red) becomes 25/64 = 0.3906. Switch to fractions to see these exact values.
Keep the diagram readable
A diagram holds up to 64 outcomes, which is plenty for textbook problems; beyond that a tree stops helping and a table or a formula does better. For counts of successes in repeated independent trials, use the Binomial Distribution Calculator instead of drawing every path.
Frequently Asked Questions
- How do I make a probability tree diagram?
- Draw one branch for each possible first outcome and write its probability on it. From the end of each branch, draw the possible second outcomes with their (conditional) probabilities, and continue for each stage. The probabilities leaving any node must add to 1. Multiply along a path to get the probability of that outcome.
- How do I calculate probability from a tree diagram?
- Multiply the probabilities along the path for an outcome (P(Rain and Late) = 0.3 × 0.6 = 0.18). For an event that covers several paths, add their probabilities (P(Late) = 0.18 + 0.14 = 0.32). Tick the outcomes in the table to do the addition automatically.
- How is a tree different with and without replacement?
- With replacement the items go back, so every draw has the same probabilities and the draws are independent. Without replacement each draw changes what is left, so the second-stage probabilities depend on the first result. With 5 red and 3 blue items, the second draw is red with 4/7 after a red and 5/7 after a blue.
- Why do my branches need to add to 1?
- Because they list everything that can happen at that point: one of the branches must occur. If they add to less than 1 an outcome is missing; to more, outcomes overlap. Leave one probability blank and the maker fills in the remainder so you only type the others.
- Can I type fractions and percentages?
- Yes. Use 3/10, 0.3 or 30%, in any mix. The maker keeps them as exact fractions, so 1/3 + 1/3 + 1/3 is exactly 1. Choose "Fractions" under the tree to read every branch and outcome as a reduced fraction instead of a decimal rounded to four places.
- How do I use a tree diagram in an APA paper?
- Tick "APA style figure" to take the title out of the image: the figure number is set in bold and the title in italics above the picture, as in APA 7, and an optional note goes below it. Then download the PNG or SVG and insert it in your document, referring to it as Figure 1 in the text.