Resolving the Boy-or-Girl Paradox with Simulation

“I have two kids, and at least one of them is a boy,” a stranger at the conference coffee cart says to you.

Most people nod politely and wonder why this matters. A few of us freeze, caffeine forgotten, and ask the only sensible question:

What’s the probability that the other child is also a boy?

Instinct shouts ½. Mathematics replies ⅓.

The mismatch sparks the Boy-or-Girl paradox — a probability riddle that survives endless explainers, lectures, and Twitter wars. Below, I’ll dissect the puzzle, its infamous variants, and the real villain behind the confusion: vague language. Then I’ll show why coding up a simulation is the fastest way to stop arguing and start understanding.

Probability’s favourite booby‑trap

Probability paradoxes feel like they’re exposing holes in math. They aren’t. They expose holes in storytelling. Human language happily blurs key details — details that change the answer. Formal probability, on the other hand, demands microscopic precision. What exactly happened? How exactly did we learn it? Any wiggle room invites multiple “correct” answers to what sounds like the same question.

The Boy‑or‑Girl paradox is a masterclass in this ambiguity. Tiny tweaks to the setup…