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 0.13, the probability that the car was manufactured by a domestic company is 0.66, and the probability that the new car needs a warranty repair and was manufactured by a domestic company is 0.047. 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? (do not round.)

Explanation:

Step1: Identify given probabilities

Let \( P(W) \) be the probability a car needs warranty repair, \( P(D) \) be the probability a car is domestic, and \( P(W \cap D) \) be the probability a car needs warranty repair and is domestic. We know \( P(W) = 0.13 \), \( P(D) = 0.66 \), \( P(W \cap D)=0.047 \). Wait, no—wait, the problem is part (a): "What is the probability that a new car selected at random needs a warranty repair?" Wait, actually, maybe we need to use the law of total probability? Wait, no, wait the problem says "the probability that the new car needs warranty repair is 0.13"? Wait, no, let's re-read.

Wait, the text: "the probability that the new car needs warranty repair is 0.13"—wait, no, let's parse the text again.

"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 0.13, the probability that the car was manufactured by a domestic company is 0.66, and the probability that the new car needs a warranty repair and was manufactured by a domestic company is 0.047. 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?"

Wait, but it says "the probability that the new car needs warranty repair is 0.13"—so is that the answer? Wait, no, maybe I misread. Wait, no, maybe the 0.13 is \( P(W) \), so the probability that a new car needs a warranty repair is 0.13? Wait, but that seems too straightforward. Wait, maybe the problem is that maybe we need to calculate it using the contingency table, but let's check.

Wait, let's define:

Let \( W \) be the event that a car needs warranty repair, \( D \) be the event that a car is domestic.

We know:

\( P(W) = 0.13 \) (given: "the probability that the new car needs warranty repair is 0.13")

Wait, but maybe that's the case. So the probability that a new car selected at random needs a warranty repair is 0.13.

Wait, but maybe I made a mistake. Wait, let's check the numbers again. The problem says "the probability that the new car needs warranty repair is 0.13"—so that's the probability for part (a).

Answer:

\( 0.13 \)