Each year, ratings are compiled concerning the performance of new cars during the first 90 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 .08, the probability that the car is manufactured by a company based in country X is .60, and the probability that the new car needs a warranty repair and was manufactured by a company based in country X is .025. Use this information to answer (a) Through (D)

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?

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?

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

Yes or NO or Not enough information

Answer:

1. 0.0417

2. 0.1375

3. no

Step-by-step explanation:

lets define:

A as the probability that a car needs a warranty repair.

B as probability taht the car is manufactured by a company that is based in country X

we have the

prob(A) = 0.08

prob(B) = 0.60

prob(A∩B) = 0.025

a. we are to calculate the probability taht a car manufactured in country X needs a warranty repair.

= p(AIB) =

[tex]P(\frac{AnB}{p(B)}) \\[/tex]

= 0.025/0.60

= 0.0417

2. Probability that car needs warranty repair given it was not manufactured in country X.

P(AIB')

= p(A∩B')/P(B')

= 0.08-0.025/1-0.60

= 0.055/0.40

= 0.1375

3. no, Need for warranty repair and location are not independent

The probability that the car needs warranty repair is 0.0417, the probability that the car needs warranty repair was not manufactured in company X is 0.1375 and no, there is no need for warranty repair and the location of the company manufacturing the car is not independent.

Given :

a) The probability that the car needs warranty repair is given by:

[tex]\rm P(A|B) = \dfrac{ P(A\cap B)}{P(B)}[/tex]

[tex]\rm P(A|B) = \dfrac{0.025}{0.60}[/tex]

P(A|B) = 0.0417

b) The probability that the car needs warranty repair was not manufactured in company X is given by:

[tex]\rm P(A|B') = \dfrac{ P(A\cap B')}{P(B')}[/tex]

[tex]\rm P(A|B') = \dfrac{0.08-0.025}{1-0.60}[/tex]

P(A|B') = 0.1375

c) No, there is no need for warranty repair and the location of the company manufacturing the car is not independent.

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