Question: A company hires people in four different groupings to install automobile carpet. The company has found that people with at least ten years experience generally produce products that are defective 1% of the time; people with five to ten years of experience, 3% of the time; people with one to five years experience, 5.7% of the time; and people with less than one year, 11.3% of the time. Of the total workforce preparing carpet, those with ten or more years comprise 45% of the total; those with five to ten years, 37%; those with one to five years, 7%; and those with less than one year, 11%. For each of these categories, calculate the probability that a defective installation was done by a worker in that group.