Condition on a Chosen Rabbit Losing
Company: Sig
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
# Condition on a Chosen Rabbit Losing
Three rabbits compete in a race, and exactly one rabbit wins. The least athletic rabbit wins with probability `1/13`. Before the race, you choose one rabbit uniformly at random to support, independently of the race outcome. The rabbit you chose does not win.
What is the conditional probability that you chose the least athletic rabbit? Express the answer as a fraction in simplest form.
### What a Strong Answer Covers
- The joint probability of choosing the least athletic rabbit and observing it lose.
- The total probability that a uniformly selected rabbit loses.
- A conditional-probability ratio that does not assume equal win chances.
- Fraction simplification.
### Follow-up Questions
- Why are the individual win probabilities of the other two rabbits unnecessary?
- How would the answer change if the rabbit were selected with nonuniform probabilities?
Overview: Compute the chance that a uniformly chosen rabbit was the least athletic after learning that it lost. The solution uses joint and total loss probabilities, avoids assuming equal race strengths, and derives the reduced conditional probability 6/13.
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