Tuesday Boy Problem
Updated 2026-08-08
INTRODUCTION
English translation pending.
CORE DEFINITION
The Tuesday boy problem asks: given that a family has two children and at least one is a boy born on a Tuesday, what is the probability that both are boys? The answer is 13/27, not 1/2 or 1/3. Popularized by Gary Foshee at a conference, the puzzle is a variant of the boy-girl paradox. Adding the seemingly irrelevant day-of-week detail shrinks the sample space unevenly, because a boy born on Tuesday is more likely to appear in mixed-gender families than naive intuition assumes. The answer depends on the exact protocol by which the information was obtained.
SCAFFOLDING EFFECT
Reduce cognitive load
- Enumerate outcomes: list the sample space explicitly instead of estimating probabilities by feel. - Check conditionals: ask exactly which information was revealed, and how, before computing. - Model protocols: distinguish at least one from a randomly chosen child, since they give different answers.
Anchor fast decisions
Probability depends on how much of the sample space each piece of information eliminates. Requiring at least one boy removes only the two-girl families, leaving three equally likely cases. Adding born on Tuesday removes cases unevenly: two-boy families have more chances to contain a Tuesday boy than mixed families do, so the surviving set shifts toward boy-boy pairs. The counterintuitive jump comes from that unequal elimination, not from the day itself.
MINIMUM ACTION
In progress 0/1Practice this model in one real situation:
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Source support: Explicit
- en.wikipedia.orghttps://en.wikipedia.org/wiki/Boy_or_girl_paradoxverified
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