Martin Gardner's Mistake

TL;DR

This paper discusses the common misconceptions in the Two-Children problem, highlights Martin Gardner's correction, and analyzes the viral Tuesday-Child variation to clarify the correct probabilistic reasoning.

Contribution

It clarifies Gardner's correction and provides a detailed discussion of the Tuesday-Child variation, addressing widespread misunderstandings in the problem.

Findings

Gardner's correction clarifies the probability calculation

The Tuesday-Child variation perpetuates common misconceptions

The paper promotes accurate understanding of the problem's logic

Abstract

When Martin Gardner first presented the Two-Children problem, he made a mistake in its solution. Later he corrected the mistake in another publication, but unfortunately his incorrect solution is more widely known than his correction. In fact, a Tuesday-Child variation of this problem went viral in 2010, and the same flaw keeps reappearing in solutions for that problem as well. In this article, I would like to popularize Martin Gardner's correction and conduct a detailed discussion of the new problem.