Witness Reliability and Bayes' Theorem
A murder has been committed. A witness claims the murderer drove a red car. In this city, all cars are either red or blue, with a fraction $r$ of all cars being red. The witness correctly identifies the color of a car with probability $a$ (and is wrong with probability
-a$), regardless of the car's actual color.
Given the witness's statement that the car was red, what is the probability the car was actually red?
Evaluate for $r = 13/20$ and $a = 3/5$.
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