Suppose the data below represent, in thousands, the type of health insurance coverage of people by age. Determine P(< 18 years old) and P(< 18 years old | no health insurance). Are the events "<18 years old" and "no health insurance" independent? < 18 41,475 Age 45-64 57,316 18 44 > 64 27,568 Total 197,289 Private health insurance Government health insurance No health insurance Total 70,930 21,377 14,343 10,246 39,899 85,865 6,474 69,326 27,952 113,225 12,582 80,144 696 68,163 47,704 330,858 P(< 18 years old) -D (Round to three decimal places as needed.) P(< 18 years old | no health insurance) = (Round to three decimal places as needed.) Are the events"< 18 years old" and "no health insurance" independent? No O Yes

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The data table presented represents, in thousands, the type of health insurance coverage of people by age. The categories are divided by age groups: under 18, 18-44, 45-64, and over 64. The table includes three types of health insurance: Private health insurance, Government health insurance, and No health insurance. The totals for each category are provided.

### Age Distribution and Insurance Type (in thousands):

- **Private health insurance:**
  - < 18: 41,475
  - 18-44: 70,930
  - 45-64: 57,316
  - > 64: 27,568
  - Total: 197,289

- **Government health insurance:**
  - < 18: 21,377
  - 18-44: 14,343
  - 45-64: 12,526
  - > 64: 39,899
  - Total: 85,865

- **No health insurance:**
  - < 18: 6,474
  - 18-44: 27,952
  - 45-64: 12,582
  - > 64: 696
  - Total: 47,704

- **Overall Totals:**
  - < 18: 69,326
  - 18-44: 113,225
  - 45-64: 80,144
  - > 64: 68,163
  - Grand Total: 330,858

### Probability Calculation Tasks:

1. **Determine P(< 18 years old):**
   - The reader is prompted to calculate this probability (rounded to three decimal places).

2. **Determine P(< 18 years old | no health insurance):**
   - The reader is prompted to calculate this conditional probability (rounded to three decimal places).

3. **Evaluate Independence:**
   - The reader needs to assess whether the events "< 18 years old" and "no health insurance" are independent and choose between "No" or "Yes".
Transcribed Image Text:The data table presented represents, in thousands, the type of health insurance coverage of people by age. The categories are divided by age groups: under 18, 18-44, 45-64, and over 64. The table includes three types of health insurance: Private health insurance, Government health insurance, and No health insurance. The totals for each category are provided. ### Age Distribution and Insurance Type (in thousands): - **Private health insurance:** - < 18: 41,475 - 18-44: 70,930 - 45-64: 57,316 - > 64: 27,568 - Total: 197,289 - **Government health insurance:** - < 18: 21,377 - 18-44: 14,343 - 45-64: 12,526 - > 64: 39,899 - Total: 85,865 - **No health insurance:** - < 18: 6,474 - 18-44: 27,952 - 45-64: 12,582 - > 64: 696 - Total: 47,704 - **Overall Totals:** - < 18: 69,326 - 18-44: 113,225 - 45-64: 80,144 - > 64: 68,163 - Grand Total: 330,858 ### Probability Calculation Tasks: 1. **Determine P(< 18 years old):** - The reader is prompted to calculate this probability (rounded to three decimal places). 2. **Determine P(< 18 years old | no health insurance):** - The reader is prompted to calculate this conditional probability (rounded to three decimal places). 3. **Evaluate Independence:** - The reader needs to assess whether the events "< 18 years old" and "no health insurance" are independent and choose between "No" or "Yes".
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