Question

A country conducts a study on new cars within the first 90 days of use. The cars have been categorized according to whether the car needs a​ warranty-based repair​ (yes or​ no) and the​ car's origin​ (domestic or​ foreign). Based on the data​ collected, the probability that the new car needs warranty repair is 0.14, the probability that the car was manufactured by a domestic company is 0.62,and the probability that the new car needs a warranty repair and was manufactured by a domestic company is 0.032. Construct a contingency table to evaluate the probabilities of a​ warranty-related repair. Complete parts​ (a) through​ (e). (round to 3 decimal places if necessary) a. What is the probability that a new car selected at random does not need a warranty ​repair? b. What is the probability that a new car selected at random does not need a warranty repair and was manufactured by a domestic​ company? c. What is the probability that a new car selected at random needs a warranty repair or was manufactured by a domestic ​company? d. What is the probability that a new car selected at random needs a warranty repair or was made by a foreign​ company? e. Given that the car was made by a foreign company, what is the probability of the car needs a warranty repair?

Answer 1

from above:

	domestic	Foreign	total
yes	0.032	0.108	0.14
no	0.588	0.272	0.86
total	0.62	0.38	1

a) probability that a new car selected at random does not need a warranty ​repair =1-0.14 =0.86

b_)

probability that a new car selected at random does not need a warranty repair and was manufactured by a domestic​ company =0.588

c)

probability that a new car selected at random needs a warranty repair or was manufactured by a domestic ​company =0.032+0.108+0.588 =0.728

d) probability that a new car selected at random needs a warranty repair or was made by a foreign​ company =0.032+0.108+0.272 =0.412

e)

Given that the car was made by a foreign company, what is the probability of the car needs a warranty repair =0.108/0.38 =0.284