Suppose that a cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. Suppose that 85% of the cabs in the city are Green and 15% are Blue. A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colors 80% of the time and failed 20% of the time. Which is more probable?
- The cab involved in the hit-and-run accident was green.
- The cab involved in the hit-and-run accident was blue.
Below is an excellent video from 3blue1brown discussing Bayes Theorem, the base-rate fallacy, and the conjunction fallacy: