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The problem you're working on involves probability based on the given data. Let's break it down:

The question states that:
- A total of 110 workers were surveyed in two departments.
- Of these workers, 46 were in Department A.
- 6 workers in Department A earned more than $80,000.
- 40 workers in Department B earned $80,000 or less.

### Part (a) asks: 
**Find the probability that a worker is in Department A and earning $80,000 or less.**

1. First, calculate how many workers in Department A earn $80,000 or less. Since 6 workers in Department A earn more than $80,000, the number of workers earning $80,000 or less in Department A is:
\[
46 - 6 = 40 \text{ workers}.
\]

2. Now, calculate the probability. The total number of workers is 110. So, the probability that a worker is in Department A and earns $80,000 or less is:
\[
P(\text{Department A and earning $80,000 or less}) = \frac{40}{110}.
\]

Let's simplify this:
\[
\frac{40}{110} \approx 0.36.
\]

So, the probability is **0.36** (rounded to two decimal places).

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Let me know if you'd like more detailed steps or explanations!

### Questions for practice:
1. What is the probability that a randomly selected worker is from Department B?
2. How many workers in total earn more than $80,000?
3. What is the probability that a worker earns more than $80,000 in any department?
4. How would the probability change if the number of workers earning more than $80,000 in Department A was reduced by half?
5. If another department is added with 30 workers, how would that affect the probabilities?

**Tip:** Always check if the total population is segmented properly before calculating probabilities based on conditions.

Find the probability that a worker is in Department A earning $80,000 or less. The following data were gathered for 110 workers in two departments. Of these workers, 46 were in Department A, 6 workers in Department A earned more than $80,000, and 40 workers in Department B earned $80,000 or less.

Find the probability that a worker is in Department A earning $80,000 or less based on a dataset of 110 workers in two departments. Learn key probability concepts and see step-by-step calculations. Ideal for students in Grades 9-12.

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