3. A company sells a certain type of car, which it assembles in one of four possible locations. Plant I supplies 20%; plant II, 24%; plant III, 25%; and plant IV, 31%. A customer buying a car does not know where the car has been assembled, and so the probabilities of a purchased car being from each of the four plants can be thought of as being 0.20, 0.24, 0.25, and 0.31. Each new car sold carries a 1-year bumper-to-bumper warranty. P( claim | plant I )= 0.05, P( claim | plant II ) = 0.11 P( claim | plant III ) = 0.03, P( claim | plant IV) = 0.08 a) Find the probability for car assembled in plant I and receiving a claim on its warranty. b) Find probability for car which is claimable on its warranty. (5 marks)