If about 3000 of every recall model of a vehicle actually need rework, what is the probability that your (recalled) car will not need a rework if there are 120000 cars of that model sold, and if 1000 of them are already off the road (this is a monkey wrench!). State your assumptions.
To find the probability that your car will not need a rework, we need to make a few assumptions:
1. We assume that the probability of needing a rework is consistent across all cars of the same model.
2. We assume that the 3000 cars that need rework are representative of all the recalled cars of that model.
Based on these assumptions, let's calculate the probability:
Step 1: Determine the number of cars that have already been recalled and off the road:
120,000 (total cars) - 1,000 (off the road cars) = 119,000 cars
Step 2: Calculate the proportion of cars that need rework:
3,000 (cars that need rework) / 119,000 (total cars) = 0.0252
Step 3: Calculate the probability of a car not needing rework:
1 - 0.0252 = 0.9748
Therefore, the probability that your car will not need a rework is approximately 0.9748, or 97.48%.
Please note that these calculations are based on the assumptions mentioned above and may not reflect the actual probability in real-world scenarios.