The Faulty Car

What this conditional-probability interview question tests

This is an easy probability question that asks you to apply Bayes' theorem — a cornerstone tool in quant interviews. You are given the probability of failure modes and their independence, and must work backwards from an observed outcome (the car broke down) to infer the probability of a specific cause.

The key challenge is setting up the problem correctly: identifying what you know (marginal failure rates and independence), what you observe (the car failed), and what you need to find (the probability of one failure mode given that failure occurred). Problems of this type reward clear thinking about conditional vs. marginal probability and careful application of the multiplication and addition rules.

• Bayes' theorem and conditional probability
• Independence and joint probabilities
• The law of total probability