Skip to content
ENExplore Calculators

Tree Diagram Probability Calculator

Work out tree diagram probability instantly with clear inputs, formula shown and shareable results.

About Tree Diagram Probability Calculator

In a probability tree the chance of a particular path is the product of the branch probabilities along it. Summing over paths gives compound event probabilities, and the branch probabilities at each node must total 1.

Formulas

Path probability

multiply the branch probabilities along the path

Expected successes

E = Σpᵏ across independent stages

Worked example

With the default values below, Tree Diagram Probability Calculator returns Probability of following all three branches of 0.1680000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First branch probabilityaccepts 0–100 %
60 %
Second branch probabilityaccepts 0–100 %
40 %
Third branch probabilityaccepts 0–100 %
70 %

Results

Probability of following all three branches
0.1680000000
Probability of the opposite path
0.0720000000
Probability of at least one success
0.9280000000
Expected number of successes
1.700000

Step by step

  1. 1Values used
  2. 2Path probability
  3. 3Expected successes
  4. 4Probability of following all three branches= 0.1680000000
  5. 5Probability of the opposite path= 0.0720000000
  6. 6Probability of at least one success= 0.9280000000
  7. 7Expected number of successes= 1.700000

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 10 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For branches 0.6, 0.4 and 0.7?

The full success path has probability 0.168, and at least one success occurs with probability 0.928.

Why multiply along a path?

Each step is conditional on reaching that node, and the multiplication rule chains those conditionals together.

Related Calculators

Tree Diagram Probability Calculator | Calcrivo