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Use the data in the table below, which shows the employment status of individuals in a particular town by age group.

A person from the town is randomly selected; what is the probability that the individual is employed full-time, given that they are between 18 and 49 years of age?

To solve the problem, we need to calculate the probability that a randomly selected individual is employed full-time, given that they are between 18 and 49 years of age. This means we are focusing on individuals in the 18-25, 26-34, and 35-49 age groups.

### Step 1: Find the total number of people aged 18 to 49.
We need to sum up all the individuals in the 18-25, 26-34, and 35-49 age groups across all employment categories.

- **18-25**: \( 195 \text{ (full-time)} + 203 \text{ (part-time)} + 148 \text{ (unemployed)} = 546 \)
- **26-34**: \( 348 \text{ (full-time)} + 75 \text{ (part-time)} + 27 \text{ (unemployed)} = 450 \)
- **35-49**: \( 581 \text{ (full-time)} + 179 \text{ (part-time)} + 106 \text{ (unemployed)} = 866 \)

So, the total number of individuals aged 18-49 is:
\[
546 + 450 + 866 = 1862
\]

### Step 2: Find the total number of people employed full-time in the 18-49 age range.
Now, sum up the full-time employed individuals in the 18-25, 26-34, and 35-49 age groups:

- **18-25**: 195
- **26-34**: 348
- **35-49**: 581

The total number of people employed full-time between 18 and 49 is:
\[
195 + 348 + 581 = 1124
\]

### Step 3: Calculate the conditional probability.
The conditional probability is the number of people employed full-time in the 18-49 age range divided by the total number of people in that age range:

\[
P(\text{full-time} | \text{age 18-49}) = \frac{1124}{1862} \approx 0.6035
\]

Thus, the probability that a randomly selected individual between 18 and 49 years old is employed full-time is approximately **0.6035** or **60.35%**.

Would you like more details or further clarifications?

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Here are 5 related questions for practice:

1. What is the probability that a randomly selected person is part-time employed, given that they are between 18 and 49 years of age?
2. What is the probability that a randomly selected individual is unemployed, given that they are between 18 and 49 years of age?
3. What is the total probability that a randomly selected individual from the entire population (all age groups) is employed full-time?
4. If a person is randomly selected from the 50+ age group, what is the probability that they are employed full-time?
5. What is the probability that a randomly selected person is employed either full-time or part-time, given that they are between 18 and 25 years old?

### Tip:
When working with conditional probabilities, always focus on narrowing down the total population to the specific condition before calculating the favorable outcome probability.

A person from the town is randomly selected; what is the probability that the individual is employed full-time, given that they are between 18 and 49 years of age?

Calculate the probability that a person randomly selected from the town is employed full-time, given that they are between 18 and 49 years old. The solution involves using conditional probability and includes detailed steps for a clear understanding.

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