The police investigates a crime scene and want to find out which car the criminals used. They find traces of a special car varnish which is often found on Italian sports cars. 80 % of all Ferraris, but only 1 % of all cars in the country have this varnish. However, only 0.01 % of all cars in the country are Ferraris. On the other hand, 5 % of all cars in the country are VW Golf, but this varnish is used for only 2 % of all Golfs. Use Bayes' rule to calculate the likelihood for both cars and decide which car the police should look for. Exactly define all symbols that you use.
The police later also finds tire tracks. This kind of tires is used in 75 % of all Ferraris, but only in 1 % of all VW Golf. Update the probabilities for both car types. Which car should the police look for now, and how much more likely is this car type than the other one? Write down all your assumptions and exactly define all symbols that you use.