# When intuition fails in assessing conditional risks: the example of the frog riddle

## TL;DR

This paper examines how the way information is presented affects understanding of conditional risks, using the frog riddle as a case study, and proposes a generalized, logically consistent solution.

## Contribution

It highlights the importance of information presentation in conditional probability puzzles and offers a new, consistent solution to the frog riddle.

## Key findings

- Information framing influences intuitive reasoning in probability puzzles.
- The original solution to the frog riddle is inconsistent due to presentation issues.
- A generalized, logically consistent solution is proposed.

## Abstract

Recently, the educational initiative TED-Ed has published a popular brain teaser coined the 'frog riddle', which illustrates non-intuitive implications of conditional probabilities. In its intended form, the frog riddle is a reformulation of the classic boy-girl paradox. However, the authors alter the narrative of the riddle in a form, that subtly changes the way information is conveyed. The presented solution, unfortunately, does not take this point into full account, and as a consequence, lacks consistency in the sense that different parts of the problem are treated on unequal footing. We here review, how the mechanism of receiving information matters, and why this is exactly the reason that such kind of problems challenge intuitive thinking. Subsequently, we present a generalized solution, that accounts for the above difficulties, and preserves full logical consistency. Eventually, the relation to the boy-girl paradox is discussed.