Question

In: Math

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?

A.

No

B.

Yes

C.

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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