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?
.0.603

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Full-time	Part-time	Unemployed
0-17	 24	164	371
18-25	190	203	148
26-34	348	 69	 27
35-49	581	179	106
50+	443	162	173

To solve this problem, we need to calculate the conditional probability that an individual is employed full-time given that they are between 18 and 49 years of age. 

The formula for conditional probability is:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Here, \( A \) is the event that the person is employed full-time, and \( B \) is the event that the person is between 18 and 49 years old.

### Step 1: Calculate the total number of people between 18 and 49 years old.

From the table, we sum the people in the age groups 18-25, 26-34, and 35-49:

\[
\begin{align*}
\text{Total between 18-25} &= 190 + 203 + 148 = 541, \\
\text{Total between 26-34} &= 348 + 69 + 27 = 444, \\
\text{Total between 35-49} &= 581 + 179 + 106 = 866.
\end{align*}
\]

Total number of people between 18 and 49:

\[
541 + 444 + 866 = 1851.
\]

### Step 2: Calculate the number of people employed full-time between 18 and 49 years old.

From the table, we sum the full-time employed individuals in the age groups 18-25, 26-34, and 35-49:

\[
\begin{align*}
\text{Full-time between 18-25} &= 190, \\
\text{Full-time between 26-34} &= 348, \\
\text{Full-time between 35-49} &= 581.
\end{align*}
\]

Total number of people employed full-time between 18 and 49:

\[
190 + 348 + 581 = 1119.
\]

### Step 3: Calculate the conditional probability.

The conditional probability that an individual is employed full-time given that they are between 18 and 49 years of age is:

\[
P(\text{Full-time}|\text{18-49}) = \frac{\text{Number of full-time employed between 18-49}}{\text{Total number of people between 18-49}} = \frac{1119}{1851}.
\]

### Step 4: Simplify the fraction.

Calculating the decimal value:

\[
\frac{1119}{1851} \approx 0.604.
\]

Therefore, the probability that an individual is employed full-time given that they are between 18 and 49 years of age is approximately \(0.604\).

Would you like any more details or have any questions?

Here are some questions you might want to ask:

1. How do you determine conditional probability?
2. What if the data includes more categories?
3. How does this probability change if more age groups are added?
4. Can you explain how to calculate probabilities for part-time or unemployed statuses?
5. How would the calculation change if given more complex conditions?

**Tip:** Always ensure you understand the conditions and categories in probability problems, as they can significantly affect your calculations.

Learn how to calculate the conditional probability of an individual being employed full-time given their age group (18-49 years). This problem involves using statistical data to determine probabilities and is suitable for students studying probability in Grades 10-12.

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