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 0.09​, he probability that the car is manufactured by a company based in country X is 0.60​, 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?

nothing

Answer 1

Solution:

Given data

Let A = The event that the new car needs a warranty repair

B = The event that the car is manufactured by a company based in country x

P(B) = 0.60

P(A) = 0.09

P(A and B) = 0.025

We have to find  the probability that the car needs warranty​ repair:

we know that

The formula of P(A|B) is given by

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

P(A|B) = 0.025 /0.60

P(A|B) = 0.0417

Therefore the probability that the car needs warranty repair is 0.0417