The losing rabbit

What this conditional-probability interview question tests

This is a medium-difficulty probability question that requires you to apply Bayes' theorem under incomplete information. It appears frequently in quant interviews because it rewards rigorous reasoning about how new evidence updates your beliefs about hidden states.

To solve it, you must first infer the win probabilities of all three rabbits from the constraint that exactly one wins and the least athletic has a 1/15 chance. Then you condition on the observed outcome—your chosen rabbit lost—and use Bayesian reasoning to compute the posterior probability of a specific identity. The trap is conflating the prior (your random choice) with the posterior (after observing the loss).

• Bayes' theorem and posterior inference
• Prior vs. posterior probabilities
• Symmetry and parameter solving under constraints
• The law of total probability