easy Probability
A release-checked easy problem for training Bayes' Theorem, Conditional Probability.
Someone was murdered! A witness claims that the murderer had a red car. Suppose that witnesses are correct with probability $a$. In this particular city, all cars are red or blue, of which $100r\%$ of them are red. Taking into account the witness statement, what is the probability that the killer actually had a red car with $r= 13/20$ and $a = 3/5$?
This Probability problem is tagged Bayes' Theorem, Conditional Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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