Question

Each​ year, ratings are compiled concerning the performance of new cars during the first 100 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 0.05​, the probability that the car is manufactured by a company based in country X is 0.90​, and the probability that the new car needs a warranty repair and was manufactured by a company based in country X is 0.025. 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?

Answer 1

Answer :

given data :-

the probability that the new car needs a warranty repair = 0.05

   p(A) = 0.05

the car is manufactured by a company based in country X = 0.90​

p(B) = 0.90

the probability that the new car needs a warranty repair and was manufactured by a company based in country X =  0.025

p(A and B) = 0.025

=> now we need to find out the probability that the car needs warranty​ repair...?

we know that

p(A|B) = p(A and B)/p(B)

p(A|B) = 0.025/0.90

p(A|B) = 0.0277

  the probability that the car needs warranty​ repair is : 0.0277