To determine the probability that the first survey selected indicates four children in the family and the second survey selected indicates one child in the family, we'll follow these steps:
1. Calculate the Total Number of Surveys:
To start, you need to find out the total number of surveys conducted. According to the table:
- One child: 9 surveys
- Two children: 18 surveys
- Three children: 22 surveys
- Four children: 8 surveys
- Five or more children: 3 surveys
Adding these together gives the total number of surveys:
[tex]\[
9 + 18 + 22 + 8 + 3 = 60
\][/tex]
2. Calculate the Probability for Each Selection:
- Probability that the first survey indicates four children:
[tex]\[
\text{Probability (four children)} = \frac{8}{60} = 0.13333333333333333
\][/tex]
- Probability that the second survey indicates one child:
[tex]\[
\text{Probability (one child)} = \frac{9}{60} = 0.15
\][/tex]
3. Determine the Combined Probability:
The surveys are chosen with replacement, meaning the selections are independent events. Therefore, the combined probability is the product of the individual probabilities:
[tex]\[
\text{Combined Probability} = \left(\frac{8}{60}\right) \times \left(\frac{9}{60}\right) = 0.02
\][/tex]
4. Convert to a Fraction:
To convert the combined probability into a fraction:
[tex]\[
0.02 = \frac{2}{100} = \frac{1}{50}
\][/tex]
Thus, the probability that the first survey chosen indicates four children in the family and the second survey indicates one child in the family is:
[tex]\[
\boxed{\frac{1}{50}}
\][/tex]
