Math Problem Statement

If a person is randomly chosen from the town's population, what is the probability that the person is under 18 or employed part-time?

Solution

To calculate the probability that a randomly chosen person is under 18 or employed part-time, we first need to identify the relevant data from the table and then compute the total population and the favorable outcomes.

Step 1: Extract the relevant data

From the table:

  • Under 18 (Age group 0–17):

    • Full-time: 21
    • Part-time: 169
    • Unemployed: 250
    • Total for this group = 21+169+250=44021 + 169 + 250 = 440
  • Part-time employment in other age groups:

    • 18–25: 199
    • 26–34: 69
    • 35–49: 192
    • 50+: 163
    • Total part-time employed (excluding under 18) = 199+69+192+163=623199 + 69 + 192 + 163 = 623

Step 2: Calculate the total population

The total population includes all age groups across all employment statuses:

  • 0–17: 440
  • 18–25: 287+199+189=675287 + 199 + 189 = 675
  • 26–34: 291+69+24=384291 + 69 + 24 = 384
  • 35–49: 430+192+166=788430 + 192 + 166 = 788
  • 50+: 371+163+235=769371 + 163 + 235 = 769

The total population is: 440+675+384+788+769=3056440 + 675 + 384 + 788 + 769 = 3056

Step 3: Calculate favorable outcomes

Favorable outcomes include:

  1. Everyone under 18: 440 people.
  2. Part-time employed (excluding under 18): 623 people.

Thus, the total number of favorable outcomes is: 440+623=1063440 + 623 = 1063

Step 4: Calculate the probability

The probability is the ratio of favorable outcomes to the total population: 106330560.3479\frac{1063}{3056} \approx 0.3479

So, the probability that a randomly chosen person is either under 18 or employed part-time is approximately 0.348 or 34.8%.

Would you like further details on any step or clarification?

Here are some related questions you might consider:

  1. What is the probability that a person is under 18 and unemployed?
  2. What is the probability that a person is over 50 and employed full-time?
  3. What is the probability that a person is employed part-time, regardless of age?
  4. What is the probability that a person is in the 18–25 age group and unemployed?
  5. How many people are employed full-time across all age groups?

Tip: When calculating probabilities, always ensure that you're clear on whether outcomes overlap to avoid double-counting.

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Math Problem Analysis

Mathematical Concepts

Probability
Statistics
Combinatorics

Formulas

Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 9-12