Solve Bertrand’s coin-box paradox with adjustable box priors and a uniformly observed gold or silver coin.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
Posterior box weights are proportional to prior box weight × probability of the observed coin.
Assumptions and limits
Choose a box using the entered weights, then choose one of its two coins uniformly. A host deliberately selecting a gold coin is a different observation protocol.
Worked example
Give all three boxes relative weight 1 and observe gold. Gold–gold contributes weight 1, gold–silver contributes 1/2 and silver–silver contributes zero. After normalization, the posterior all-gold probability is 2/3. Thus the other coin is gold with probability 2/3. The answer relies on randomly drawing one coin, not a host deliberately selecting a gold reveal.
Worked reading and practical questions
- Count Coin Observations, Not Just Surviving Boxes
- How Biased Box Selection Changes the Two-Thirds Answer
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
Choose a box using the entered weights, then choose one of its two coins uniformly. A host deliberately selecting a gold coin is a different observation protocol.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.