Final answer:
The probability that a car will require repairs costing more than $125 for a faulty pollution control system after an inspection is 2%, calculated by multiplying the 10% chance of having a faulty system by the 20% chance that repairs exceed $125.
Step-by-step explanation:
The student has provided a probability problem where we need to calculate the likelihood of a specific event occurring. In this case, we want to determine the probability that a car will require repairs costing more than $125 for a faulty pollution control system after an inspection.
The first piece of information tells us that 10% of cars have a faulty pollution control system. The second piece of information tells us that, of those cars with a faulty system, 20% will incur repair costs exceeding $125. To find the overall probability of a car needing repairs exceeding $125, we multiply the probability of a car having a faulty system (10%) by the probability that the repair costs will exceed $125 (20%).
Mathematically, this can be represented as:
Probability = 0.10 (probability of faulty system) * 0.20 (probability of repair cost > $125) = 0.02 or 2%
Therefore, there is a 2% probability that a car taken for inspection will require repairs costing more than $125 for the pollution control system.