The paint department in an automobile factory applies two processes when painting cars:(i) painting and (ii) polishing. The painting process is defective 20% of the time, whilethe polishing process is defective 10% of the time. Each car first goes through thepainting and then through the polishing process. Each car is inspected after it hascompleted the two processes. If either the painting or the polishing is defective, the car isreturned to a special station for rework, where the two processes are applied once again.Rework at the special station is 100% reliable (although it is also very expensive).i. What is the probability that a car is returned to the special station for rework?ii. In a batch of 1000 cars, what is the expected number of cars that will be returnedfor rework?iii. In a batch of 1000 cars, what is the probability that the number of returned cars isless than or equal to 200?iv. Let X be the number of cars in a group of 1000 cars that have painting defects.Let Y be the number of cars in a group of 1000 cars that have polishing defects.What is the distribution of X? What is the distribution of Y?v. What is the probability that the total number of defects, X+Y, is less than or equalto 300?