Most car manufacturers will have a goodwill or special policy in place to extend the original warranty of the vehicle for no cost or cost-reduced repairs. These policies are usually not made public, and are often applied to vehicle defects that surface after manufacturing. One model of vehicle was found to have defective airbags, due to a failure of the sensing system. It was estimated that the odds in favor of purchasing the vehicle with this defect were 51: 635

Question

Most car manufacturers will have a goodwill or special policy in place to extend the original warranty of the vehicle for no cost or cost-reduced repairs. These policies are usually not made public, and are often applied to vehicle defects that surface after manufacturing. One model of vehicle was found to have defective airbags, due to a failure of the sensing system. It was estimated that the odds in favor of purchasing the vehicle with this defect were 51: 635

If 12 800 vehicles of this make and model were manufactured in one year, how many will likely need the warranty work? (

Answer 1

To determine how many vehicles are likely to need warranty work, we first need to calculate the probability of a vehicle having the defect.

The odds in favor of purchasing the vehicle with the defect are 51:635, which means the probability of purchasing a defective vehicle is 51/(51+635) = 51/686 ≈ 0.0745.

Therefore, out of 12,800 vehicles manufactured, we can expect approximately 0.0745 * 12,800 ≈ 953 vehicles to have the defect and need warranty work.