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Each year, ratings are compiled concerning the performance of new cars during the first 60 days...

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 0.07, the probability that the car is manufactured by a company based in country X is 0.50, 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?

(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.)

c. Are need for warranty repair and location of the company manufacturing the car independent?

Yes

Not enough information

Solutions

Expert Solution

Given:

P(Repair) = 0.07

P(Repair AND based on country X) = 0.025

P(Company based in country X) = 0.50

P(Company did not base in country X) = 1 - 0.50 = 0.50

(a) P(Warranty repair| based in country X) that is a conditional probability.

The formula to find the conditional probability is,

The probability that the car needs warranty repair given that based in country X is 0.05

(b) P(Repair| did not based in country X) that is a conditional probability.

Using the total law of probability, we can write P(Repair) as,

P(Repair) = P(Repair AND based on country X) + P(Repair AND did not base on country X)

0.07 = 0.025 + P(Repair AND did not base on country X)

P(Repair AND did not base on country X) = 0.07 - 0.025 = 0.045

The formula of conditional probability is,

The probability that the car needs warranty repair given that did not base on country X is 0.09

(c) Two events are independent when P(A AND B) = P(A) * P(B)

Here A: Repair and B: base on country X

P(Repair AND based on country X) = 0.025

P(Repair) * P(based on country X) = 0.07 * 0.50 = 0.035

That is P(A AND B) not equal to P(A) * P(B)

Therefore, need for warranty repair and location of the company manufacturing the car are not independent.

The answer is No.

milcah answered 1 year ago

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Each​ year, ratings are compiled concerning the performance of new cars during the first 60 days...

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Each year, ratings are compiled concerning the performance of new cars during the first 60 days...