Each year, ratings are compiled concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether a car needs warranty-related repair (yes or no) and the country in which the company manufacturing a car is based (United States or not United States). Based on the data collected, the probability that the new car needs a warranty repair is 0.04, the probability that the car is manufactured by a U.S.-based company is 0.60, and the probability that the new car needs a warranty repair and was manufactured by a U.S.-based company is 0.025.
a. Suppose you know that a company based in the United States manufactured a particular car. What is the probability that the car needs a warranty repair?
b. Suppose you know that a company based in the United States did not manufacture a particular car. What is the probability that the car needs a warranty repair?
c. Are need for a warranty repair and location of the company manufacturing the car independent?