1. **Stating the problem:** We have a two-way table showing the number of men and women workers who either have a problem or no problem with wage levels for men and women doing the same job. We want to estimate the probability that the next randomly chosen adult worker falls into a certain category. 2. **Given data:** | Gender | Problem | No Problem | |--------|---------|------------| | Men | 146 | 175 | | Women | 188 | 134 | 3. **Total number of workers surveyed:** $$146 + 175 + 188 + 134 = 643$$ 4. **Calculating probabilities:** - Probability that the next worker is a man with a problem: $$P(\text{Man and Problem}) = \frac{146}{643}$$ - Probability that the next worker is a man with no problem: $$P(\text{Man and No Problem}) = \frac{175}{643}$$ - Probability that the next worker is a woman with a problem: $$P(\text{Woman and Problem}) = \frac{188}{643}$$ - Probability that the next worker is a woman with no problem: $$P(\text{Woman and No Problem}) = \frac{134}{643}$$ 5. **Explanation:** The probability of an event is the number of favorable outcomes divided by the total number of outcomes. Here, the total number of outcomes is the total number of surveyed workers (643). Each cell count represents favorable outcomes for that category. 6. **Final answers:** - $P(\text{Man and Problem}) = \frac{146}{643} \approx 0.227$ - $P(\text{Man and No Problem}) = \frac{175}{643} \approx 0.272$ - $P(\text{Woman and Problem}) = \frac{188}{643} \approx 0.292$ - $P(\text{Woman and No Problem}) = \frac{134}{643} \approx 0.208$ These probabilities estimate the chance that the next randomly chosen adult worker falls into each category.