About the Probability Tree Calculator
What is the Probability Tree Calculator?
A probability tree shows a sequence of events as branches. The first stage splits into A and not-A (A′); each of those then splits into B and not-B (B′). Multiplying along a path gives the probability of that path, and adding paths gives the probability of an outcome.
Enter P(A) and the probability of B in each branch. The calculator returns all four path probabilities, the total probability of B, the chance of not-B, and the reverse conditional probability P(A | B) using Bayes' theorem.
How to use the Probability Tree Calculator
- P(A) – probability of the first event (%) — the probability of the first-stage event, in %. (sample: 30)
- P(B | A) – B given A happened (%) — the probability of B on the A branch, in %. (sample: 80)
- P(B | A') – B given A did not happen (%) — the probability of B on the not-A branch, in %. (sample: 10)
- Press Build Probability Tree (results also refresh as you type). The result card shows the P(B) – Total Probability, along with P(A and B), P(A' and B), P(A | B) – Bayes' theorem and P(B').
Formula used
P(B) = P(A) × P(B | A) + P(A′) × P(B | A′)
- P(A′) = 1 − P(A)
- P(A and B) = P(A) × P(B | A)
- P(A | B) = P(A and B) ÷ P(B)
The four path probabilities always add up to 100%, which is a handy check.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| P(A) – probability of the first event (%) | 30 |
| P(B | A) – B given A happened (%) | 80 |
| P(B | A') – B given A did not happen (%) | 10 |
| Result | Value |
|---|---|
| P(B) – Total Probability | 31% |
| P(A and B) | 24% |
| P(A' and B) | 7% |
| P(A | B) – Bayes' theorem | 77.4194% |
| P(B') | 69% |
Tips for using the Probability Tree Calculator
- Label branches clearly: P(B | A) is “B given A”, not “A and B”.
- Use the tree for multi-step situations such as two machines producing defects, or rain affecting whether a match is played.