Each year ratings are compiled concerning new cars during th

Each year, ratings are compiled concerning new cars during the first 90 days of use. Cars are categorized according to whether a car needs warranty related repairs (yes or no)and the country in which the company manufacturing the car is based. (US based, or overseas.) The probability is that the car needs a warranty related repair is 0.4, the probability the car was manufactured by a US based company is 0.60, and the proabability that the car needs warranty related repairs and was manufactured by a US based company is 0.025. Construct a contingency table to evaluate the probabilities of a warranty related repair. What is the probability that a new car selected at ramdom:

a. Needs a warranty related repair?

b. Needs a warranty related repair and was manufactured by a US based company?

c. Needs a warranty related repair, or was manufactured by a US based comoany?

d. Needs a warranty repair or was not manufactured by a US based company

Solution

a)

Consider the table:

P(Yes) = 0.4 [answer]

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b)

P(Yes, and US) = 0.025 [answer]

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c)

P(Yes or US) = 0.025 + 0.375 + 0.575 = 0.975 [answer]

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d)

P(Yes or Overseas) = 0.025 + 0.375 + 0.025 = 0.425 [answer]