4.2.26 Question Help Each year, ratings are compiled concerning the performance

Question

4.2.26 Question Help Each year, ratings are compiled concerning the performance of new cars during the first 60 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 0.09, the probability that the car is manufactured by a company based in country X is 0.70, and the probability that the new car needs a warranty repair and was manufactured by a company based in country X is 0.035. Use this information to answer (a) through (d) below. 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? 05 (Round to three decimal places as needed.) 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? (Round to three decimal places as needed.)

Explanation / Answer

P(A) = 0.09 P(B) = 0.70

P(A and B) = 0.035

a. P(A|B) = P(A and B) / P(B)

= 0.035 / 0.70

= 0.050

b. P(A and Bc) = P(A) - P(A and B)

= 0.09 - 0.035

= 0.055

P(Bc) = 1 - 0.70 = 0.30

P(A|Bc) = P(A and Bc) / P(Bc)

= 0.055 / 0.3

= 0.183

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