Explore the conditional probability behind Bertrand's three-box paradox.
Bertrand's Box Paradox
How to use this calculator
Choose a box, observe a coin, and estimate the chance that the other coin is gold, or compare the expected outcomes over many rounds.
- Choose the calculation mode and units, when available.
- Enter values using the localized examples in the placeholders.
- Select Calculate and review the result, steps, and visualization when provided.
Formula and method
Explore the conditional probability behind Bertrand's three-box paradox.
Worked example
The placeholders provide a reproducible example. Enter them to verify the result before using your own data.
Assumptions and limitations
Values must be finite and use compatible units. Displayed decimals are rounded, while calculations retain full precision.
Frequently asked questions
What does this calculator do?
Explore the conditional probability behind Bertrand's three-box paradox.
Why do fields appear or disappear?
Dependent fields follow the selected method, shape, ingredient, or unit mode.
Are all visible formulas semantic?
Yes. Formulas and structured results use native MathML, with text retained only for labels and copying.