A potential buyer is trying to decide if a new motorcycle is…
A potential buyer is trying to decide if a new motorcycle is good or bad. The prior belief that the motorcycle is good is 50%. Then the potential buyer receives signals (test rides), where g represents a good test ride performance and b represents a bad test ride performance by the motorcycle. Also good motorcycles perform well on test rides and bad motorcycles ride poorly on test rides with 60% probability. Given that the potential buyer goes on a single good test ride, followed by two bad test rides, what is her posterior probability that the motorcycle is a good one?