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 ( in some country X or not in country X). Based on the data collected, the probability that the new car needs a warranty repair is .08, the probability that the car is manufactured by a company based in country X is .60, and the probability that the new car needs a warranty repair and was manufactured by a company based in country X is .025.

Use this information to answer (a) Through (D)

Below is the contingency table which I prepared after using the information mentioned in the question and other cells I derived on the basis of probability rules:

	Warranty related repair
Yes	No
Manufacturing a car is based	Country X	0.025	0.575	0.60
Not in Country X	0.055	0.345	0.40
		0.08	0.92	1.00

a.)Suppose you know that a company based in country X manufactured a particular car. What is the probability that the car needs warranty repair?

b.)Suppose you know that a company based in country X did not manufacture a particular car. What is the probability that the car needs warranty repair?

c.)Are need for warranty repair and location of the company manufacturing the car independent?