A country a study on new cars within the first 90 days of use. The cars have bee

Question

A country 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 0.13, the probability that the car used was manufactured by a domestic company is 0.64, and the probability that the new car needs a warranty repair and was manufactured by a domestic company is 0.043.

Construct a contingency table to evaluate the probabilities of a warranty-related repair.

Complete parts (a) through (d).

a. What is the probability that a new car selected at random needs a warranty repair?

b. What is the probability that a new car selected at random needs 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?

Explanation / Answer

Following is the completed contingency table:

(a)

The probability that a new car selected at random needs a warranty repair is

P(needs warranty repair) = 0.13

(b)

The probability that a new car selected at random needs a warranty repair and was manufactured by a domestic company is

P(needs warranty repair and manufactured by a doemstic company) = 0.043

(c)

P( manufactured by a doemstic company) = 0.64

The probability that a new car selected at random needs a warranty repair or was manufactured by a domestic company is

P(needs warranty repair and manufactured by a doemstic company)= P(needs warranty repair)+P(manufactured by a doemstic company)-P(needs warranty repair and manufactured by a doemstic company) = 0.13+0.64 - 0.043 = 0.727

(d)

The probability that a new car selected at random needs a warranty repair or was made by a foreign company is

P(needs warranty repair and manufactured by a foreign company)= P(needs warranty repair)+P(manufactured by a foreign company)-P(needs warranty repair and manufactured by a foreign company) = 0.13+0.36 - 0.087 = 0.403

Warranty based repair Yes No Total Car's origin Domestic 0.043 0.64-0.043=0.597 0.64 Foreign 0.13-0.043=0.087 0.87-0.597=0.273 0.36 Total 0.13 1-0.13=0.87 1

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