Question

Each year, ratings are compiled concerning the performance of new cars during the firs 90 days of use. Suppose that the cars have been categorized according to whether the card needs warranty- related repair( yes or no) and the country in which the company manufacturing the car is based ( united states or not united states)Based on the data collected, the probability that the new car needs a warranty repair is 0.04, the probability that the car is manufactured by a US – based company is 0.60, and the probability that the new car needs a warranty repair and was manufactured by a US- based company is 0.025. Construct a contingency table or a Venn diagram to evaluate the probabilities of a warranty- related repair. What is the probability that a new car selected at random

a. Needs a warranty- related repair?

b. Needs a warranty repair and is manufactured by a company based in the united states?

c. Needs a warranty repair or was manufactured by a US- based company?

d. Needs a warranty repair or was no manufactured by US- based company?

Answer 1

contingency table

	Warranty - related repair - Yes	Warranty - related repair - No	Total
United States	0.025	0.6-0.025 = 0.575	0.6
Not united stated	0,04-0.025 = 0.015	0.96-0.575 = 0.385	1-0.6=0.4
Total	0.04	1-0.04 = 0.96	1

a.  probability that a new car selected at random  Needs a warranty- related repair = 0.04

(Cell under Row : Total and Column : Warranty - related repair - Yes)

b. Probability that a new car selected at random Needs a warranty repair and is manufactured by a company based in the united states = 0.025

(Cell under Row : United States and Column : Warranty - related repair - Yes)

c. Probability that a new car selected at random Needs a warranty repair or was manufactured by a US- based Company

= (Probability that a new car selected at random Needs a warranty repair )

+ (Probability that a new car selected at random US- based Company)

- (Probability that a new car selected at random Needs a warranty repair and is manufactured by a company based in the united states)

Form (a) : (Probability that a new car selected at random Needs a warranty repair ) = 0.04

Probability that a new car selected at random US- based Company = 0.6

(Cell under Row :United States and Column : Total )

Form (b) : (Probability that a new car selected at random Needs a warranty repair and is manufactured by a company based in the united states) = 0.025

Probability that a new car selected at random Needs a warranty repair or was manufactured by a US- based Company

= (Probability that a new car selected at random Needs a warranty repair )

+ (Probability that a new car selected at random US- based Company)

- (Probability that a new car selected at random Needs a warranty repair and is manufactured by a company based in the united states)

= 0.04+0.6-0.025=0.615

Probability that a new car selected at random Needs a warranty repair or was manufactured by a US- based Company = 0.615

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d. Probability that a new car selected at random Needs a warranty repair or was no manufactured by a US- based Company

= (Probability that a new car selected at random Needs a warranty repair )

+ (Probability that a new car selected at random no US- based Company)

- (Probability that a new car selected at random Needs a warranty repair and is no manufactured by a company based united states)

Form (a) : (Probability that a new car selected at random Needs a warranty repair ) = 0.04

Probability that a new car selected at random no US- based Company = 0.4

(Cell under Row : not United States and Column : Total )

(Probability that a new car selected at random Needs a warranty repair and is no manufactured by a company based in the united states) = 0.015

(Cell under Row : not United States and column:  warranty -related repair-yes )

Probability that a new car selected at random Needs a warranty repair or was no manufactured by a US- based Company

= (Probability that a new car selected at random Needs a warranty repair )

+ (Probability that a new car selected at random no US- based Company)

- (Probability that a new car selected at random Needs a warranty repair and is no manufactured by a company based in the united states)

= 0.04+0.4-0.015=0.425

Probability that a new car selected at random Needs a warranty repair or was no manufactured by a US- based Company = 0.425