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(a) Calculate the following probabilities using the above data. (Round your answers to 4 decimal places.)


To calculate the probabilities using the data provided, we first need to understand the questions being asked. However, as the specific questions aren't listed, I'll assume you need common probabilities that can be derived from such data. I'll calculate the following probabilities:

1. Probability of a randomly selected woman being employed.
2. Probability of a randomly selected man being unemployed.
3. Probability of a randomly selected individual (either gender) having a Bachelor's degree or more and being employed.
4. Probability of a randomly selected woman with a high school degree being not in the labor force.
5. Probability of a randomly selected man with some college education being unemployed.
6. Probability of a randomly selected individual (either gender) being not in the labor force.

### 1. Probability of a randomly selected woman being employed:
\[ P(\text{Employed | Woman}) = \frac{\text{Number of employed women}}{\text{Total number of women}} = \frac{4985}{7771} \]

### 2. Probability of a randomly selected man being unemployed:
\[ P(\text{Unemployed | Man}) = \frac{\text{Number of unemployed men}}{\text{Total number of men}} = \frac{906}{8557} \]

### 3. Probability of a randomly selected individual (either gender) having a Bachelor's degree or more and being employed:
\[ P(\text{Employed and Bachelor's or more}) = \frac{\text{Number of women with Bachelor's degree or more employed} + \text{Number of men with Bachelor's degree or more employed}}{\text{Total number of individuals}} = \frac{921 + 708}{7771 + 8557} \]

### 4. Probability of a randomly selected woman with a high school degree being not in the labor force:
\[ P(\text{Not in labor force | Woman with HS degree}) = \frac{\text{Number of women with HS degree not in labor force}}{\text{Total number of women with HS degree}} = \frac{881}{3265} \]

### 5. Probability of a randomly selected man with some college education being unemployed:
\[ P(\text{Unemployed | Man with some college}) = \frac{\text{Number of men with some college unemployed}}{\text{Total number of men with some college}} = \frac{106}{1657} \]

### 6. Probability of a randomly selected individual (either gender) being not in the labor force:
\[ P(\text{Not in labor force}) = \frac{\text{Total number of individuals not in the labor force}}{\text{Total number of individuals}} = \frac{2066 + 1074}{7771 + 8557} \]

Now, let's calculate these probabilities:

### Calculations:
1. Probability of a randomly selected woman being employed:
\[ P(\text{Employed | Woman}) = \frac{4985}{7771} \approx 0.6415 \]

2. Probability of a randomly selected man being unemployed:
\[ P(\text{Unemployed | Man}) = \frac{906}{8557} \approx 0.1059 \]

3. Probability of a randomly selected individual having a Bachelor's degree or more and being employed:
\[ P(\text{Employed and Bachelor's or more}) = \frac{921 + 708}{7771 + 8557} = \frac{1629}{16328} \approx 0.0998 \]

4. Probability of a randomly selected woman with a high school degree being not in the labor force:
\[ P(\text{Not in labor force | Woman with HS degree}) = \frac{881}{3265} \approx 0.2698 \]

5. Probability of a randomly selected man with some college education being unemployed:
\[ P(\text{Unemployed | Man with some college}) = \frac{106}{1657} \approx 0.0639 \]

6. Probability of a randomly selected individual being not in the labor force:
\[ P(\text{Not in labor force}) = \frac{2066 + 1074}{7771 + 8557} = \frac{3140}{16328} \approx 0.1923 \]

If you have any specific questions or need further details, please let me know!

### Follow-up Questions:
1. What is the probability of a woman with some college education being employed?
2. What is the probability of a man with a high school degree being employed?
3. What is the probability of a woman with a Bachelor's degree or more being not in the labor force?
4. What is the probability of a man being employed?
5. What is the probability of a woman being unemployed?
6. What is the probability of an individual (either gender) with less than a high school education being not in the labor force?
7. What is the probability of an individual (either gender) with some college education being employed?
8. What is the probability of an individual (either gender) with a high school degree being unemployed?

### Tip:
When calculating probabilities from data, always ensure that you understand the condition and total population that you're considering. This helps in accurately interpreting and solving probability problems.

Learn how to calculate probabilities based on employment and education data. Explore probabilities such as the likelihood of employment for women, unemployment among men, and more. Detailed calculations and explanations provided.

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