To find the probability that a randomly chosen person is under 18 or employed part-time, we need to use the addition rule for probabilities:

$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

Where:

• $A$ is the event "under 18."
• $B$ is the event "employed part-time."

Step 1: Total population

The total population is the sum of all people in all categories:

$\text{Total population} = (25 + 168 + 233) + (279 + 180 + 195) + (318 + 62 + 22) + (539 + 178 + 190) + (339 + 166 + 224)$

$\text{Total population} = 3358$

Step 2: Probability of being under 18 ($P(A)$)

The total number of people under 18 is:

$\text{Under 18 total} = 25 + 168 + 233 = 426$

$P(A) = \frac{426}{3358}$

Step 3: Probability of being employed part-time ($P(B)$)

The total number of people employed part-time is:

$\text{Part-time total} = 168 + 180 + 62 + 178 + 166 = 754$

$P(B) = \frac{754}{3358}$

Step 4: Probability of being under 18 and employed part-time ($P(A \text{ and } B)$)

The number of people who are both under 18 and employed part-time is:

$\text{Under 18 and part-time} = 168$

$P(A \text{ and } B) = \frac{168}{3358}$

Step 5: Calculate $P(A \text{ or } B)$

$P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

Substitute the values: $P(A \text{ or } B) = \frac{426}{3358} + \frac{754}{3358} - \frac{168}{3358}$

$P(A \text{ or } B) = \frac{426 + 754 - 168}{3358} = \frac{1012}{3358}$

Step 6: Simplify

$P(A \text{ or } B) \approx 0.3014 \text{ or } 30.14\%$

Final Answer:

The probability that the person is under 18 or employed part-time is approximately 30.14%.

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Would you like a detailed breakdown of the steps or further clarification?

Related Questions:

1. What is the probability that a person is under 18 and unemployed?
2. What is the probability that a person is employed full-time, given they are over 50?
3. What is the probability that a person is unemployed?
4. How does the probability of being employed full-time vary by age group?
5. What is the conditional probability of being under 18, given the person is employed part-time?

Tip:

To calculate probabilities efficiently, always find the total population first—it simplifies all further steps!