Triple birthday matches in the Senate: Lies, damned lies and chatGPT

TL;DR

This paper investigates the probability of at least three senators sharing a birthday, highlighting ChatGPT's failure to answer such probability questions and providing a more accurate solution inspired by mathematical resources.

Contribution

The paper offers a corrected probability calculation for triple birthday matches in the Senate, contrasting it with ChatGPT's inadequate responses.

Findings

ChatGPT failed to answer the birthday probability question.

A more accurate probability estimate was derived.

The study emphasizes the importance of mathematical resources in AI responses.

Abstract

Our question is ``What is the probability that at least three members of the senate share the same birthday?'' Before the pandemic, I asked this question in several popular math talks I gave at universities across the country. Inspired by ChatGPT's abysmal failure to answer the question, I have recently come back to this problem and now have a more satisfactory answer, thanks in no small part to what I learned form a page of Wolfram's Math World, which I located by a Google search.