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Bertrand Box Conditional Probability Calculator — result sheet
Calculate the probability that a selected coin is gold on the other side after observing a gold face in a three-box paradox model.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: After observing gold, probability of gold on the other side=gold-gold face opportunities/(all gold face opportunities).
The model weights boxes by the number of gold faces that could have produced the observation rather than treating boxes as equally likely after selection.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Gold-gold boxes — minimum 0; maximum 1000000
- Gold-silver boxes — minimum 0; maximum 1000000
- Silver-silver boxes — minimum 0; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Gold-gold boxes | 1 |
| Gold-silver boxes | 1 |
| Silver-silver boxes | 1 |
Probability the other side is gold =2/3.
Assumptions and limits
- A box is selected uniformly and then a face is observed uniformly among its faces.
- The counts describe only the three coin-type classes.
- Selection bias, prior information, and nonuniform observation are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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