At the end of January, Daniel Litt posed a harmless probability puzzle on the social media platform X (formerly known as Twitter) – and caused a stir in a corner of the Twitterverse.
Imagine, he wrote, that you have an urn containing 100 balls, some red and some green. You can’t see inside; all you know is that someone has determined the number of red balls by drawing a number between zero and 100 from a hat. You reach into the urn and pull out a ball. It’s red. Now if you pull out a second ball, is it more likely that it will be red or green (or are the two colors equally likely)?
Of the tens of thousands of people who voted on an answer to Litt’s problem, only about 22% chose the right answer. (We’ll reveal the answer below if you want to think about it first.) In the months that followed, Litt, a mathematician at the University of Toronto, continued to confound Twitter users with a series of probability puzzles about ballot boxes and coin tosses.
His posts have sparked lively online discussions among mathematicians, computer scientists and economists – but also philosophers, financiers, sports analysts and anonymous fans. Some have joked that the puzzles distract them from their real work – “they actively slow down economic research,” as one economist put it. Others have published papers exploring the mathematical implications of the puzzles.
Litt’s online project not only underscores the enduring fascination with brain teasers. It also demonstrates the limits of our mathematical intuition and the counterintuitive nature of probabilistic thinking. As Litt wrote, there is “nothing more exciting than setting a multiple-choice problem on which 50,000 people perform significantly worse than chance.”
Quantum spoke with Litt about what makes a great puzzle and why simple probability questions can be so deceptively difficult. (Warning: Spoilers below!) The interview has been condensed and edited for clarity.
