Compare two-child conditional probabilities across at-least-one, older-child, random-child and independent-tag observation protocols.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs. Probability inputs are percentages from 0 to 100, not decimal fractions.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
For at least one boy, P(two boys | observation) = p² / [1−(1−p)²]. For a specified boy with tag chance q: p²(2q−q²) / [1−(1−pq)²].
Assumptions and limits
A two-child probability model, not a real-family prediction or a model of gender identity. Child outcomes are modeled as independent binary categories. The selection protocol is part of the question.
Worked example
With modeled boy probability 50%, selecting a family with at least one boy gives a two-boy posterior of 1/3. Specifying that the older child is a boy gives 1/2. Observing a uniformly chosen child to be a boy also gives 1/2. With the at-least-one boy-and-tag protocol and an independent tag chance of 1/7, the result becomes 13/27. Always record how the information was obtained.
Worked reading and practical questions
- Two-Child Questions: Write Down the Selection Protocol First
- The Tuesday-Boy Puzzle as an Independent-Tag Model
Browse Statistics calculators or explore other tools on the GreenCalc homepage.
Frequently asked questions
What does this calculator assume?
A two-child probability model, not a real-family prediction or a model of gender identity. Child outcomes are modeled as independent binary categories. The selection protocol is part of the question.
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.