Bayes Theorem: Speeding Problem
The probability that a teenage driver will speed is 0.8; for a twenty-something driver, the probability of speeding is 0.5; for a mature driver, 0.2. Suppose that 15% of drivers are teenagers, 20% are in their twenties, and the rest are mature. If a driver observed at random is found to be speeding, then what is the probability that this driver is a teenager?