Three randomly selected children are surveyed. The ages of the children are 2​, 3​, and 10. Assume that samples of size nequals2 are randomly selected with replacement from the population of 2​, 3​, and 10. Listed below are the nine different samples. Complete parts​ (a) through​ (d).
2​,2   2​,3   2​,10   3​,2   3​,3   3​,10   10​,2   10​,3   10​,10
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Part 1
a. For the​ population, find the proportion of odd numbers.
The proportion is

enter your response here.
​(Round to three decimal places as​ needed.)

To solve for the proportion of odd numbers in the population, we first identify the odd numbers among the ages of the children in the population (which are 2, 3, and 10).

- The population: \( \{2, 3, 10\} \)
- Odd numbers: \( 3 \)

### Step-by-step calculation:
1. **Total number of values in the population** = 3 (since we have ages 2, 3, and 10).
2. **Number of odd numbers in the population** = 1 (since only 3 is odd).

To find the proportion of odd numbers, we divide the number of odd numbers by the total number of values in the population:
\[
\text{Proportion of odd numbers} = \frac{\text{Number of odd numbers}}{\text{Total population}} = \frac{1}{3}
\]

Thus, the proportion of odd numbers is:
\[
\text{Proportion} = 0.333
\]

### Final answer:
The proportion of odd numbers in the population is **0.333**.

Would you like further details or have any questions?

Here are some related questions:
1. What is the proportion of even numbers in the population?
2. How many samples contain at least one odd number?
3. What is the mean age of the children in the population?
4. How many unique pairs of ages can be formed?
5. What is the probability of randomly selecting a sample with both ages being even?

**Tip:** Always double-check whether a sample is drawn with or without replacement, as it affects probabilities and combinations significantly.

Three randomly selected children are surveyed. The ages of the children are 2, 3, and 10. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 3, and 10. Listed below are the nine different samples. Complete parts (a) through (d).

2, 2   2, 3   2, 10   3, 2   3, 3   3, 10   10, 2   10, 3   10, 10

Part 1
a. For the population, find the proportion of odd numbers. The proportion is (Round to three decimal places as needed.)

Solve for the proportion of odd numbers in a sampled population of children's ages 2, 3, and 10. Understand key concepts like probability, population sampling, and how to calculate proportions. Suitable for students in Grades 8-10.

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