Related Repair U.S. Non-U.S. Total Yes No Total Each year, ratings are compiled
ID: 3173622 • Letter: R
Question
Related Repair
U.S.
Non-U.S.
Total
Yes
No
Total
Each year, ratings are compiled concerning the performance of new cars during the first 90-days of use. Suppose that the cars have been characterized according to weather a car needs warranty-related repair (yes or no) and country in which the company manufacture the car is based in (United States or not United States). Based on the data collected, the probability that the new car needs a warranty repair is o.040, the probability the car was manufactured by a U.S. based company is 0.60, and the probability that the new car needs a warranty repair and was manufactured by a U.S. 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 random:
Can the above table be filled with this information.
Related Repair
U.S.
Non-U.S.
Total
Yes
No
Total
Explanation / Answer
here let probability that manufactured in US =P(US)=0.6
and needs a warranty repair =P(W)=0.04
probability that the new car needs a warranty repair and was manufactured by a U.S. based company
=P(W & US)=0.025
probability that the new car needs a warranty repair and was not manufactured by a U.S. based company
=P(W &USc)=P(W)-P(W &US)==0.04-0.025=0.015
probability that a car does not need warranty =P(Wc)=1-P(W)=1-0.04=0.96
probability that the new car does not needs a warranty repair and was manufactured by a U.S. based company
=P(Wc &US)=P(Wc)-P(USc & Wc)=P(Wc)-(1-P(W)-P(US)+P(W &US)) =0.96-(1-0.6-0.04+0.025)=0.575
hence probability that the new car does not needs a warranty repair and was not manufactured by a U.S. based company =P(Wc & USc)=(1-P(W)-P(US)+P(W &US)) =(1-0.6-0.04+0.025)=0.385
hencce
U.S. Non-U.S. Total Related Repair Yes 0.025 0.015 0.04 No 0.575 0.385 0.96 Total 0.6 0.4 1