Daniel Litt's probability problems

The young mathematician Daniel Litt currently holds a position at the University of Toronto. His research usually explores the interplay between algebraic geometry and arithmetic. Yet in recent months, he has attracted attention in an entirely different field, even earning an interview with the renowned online publication Quanta Magazine.

This charismatic assistant professor regularly posts short mathematical pieces on X (formerly Twitter), and two of his probability puzzles have drawn particular interest from thousands of Internet users. Describing himself as an amateur in the field, he invited anyone willing to ponder his questions to take part in a short poll, thereby highlighting the surprisingly counterintuitive nature of situations that are nonetheless simple to describe. Above all, the ensuing good-natured debates brought together people from a wide range of backgrounds, from former students who had completely abandoned mathematics to doctoral students in the subject. Some extremely convincing arguments nevertheless turned out to be wrong. Plenty to spark lively discussions among your own friends and family!

The urn problem ---------------------

Imagine an opaque urn in front of you containing 100 red or green balls. Before you arrived, someone fixed the number k of red balls by choosing a number between 0 and 100 at random (with each number equally likely). You draw a ball at random, and it is red. You set it aside, then draw a second ball: is the second ball more likely to be red or green?