Answer :
Certainly! Let's go through each of these questions step-by-step using the data provided in the table to determine the probabilities.
### 1. Probability that someone is from the U.S.
The total number of people surveyed is [tex]\(75\)[/tex]. Out of these, [tex]\(34\)[/tex] are from the U.S.
The probability [tex]\(P(\text{from the U.S})\)[/tex] can be calculated as:
[tex]\[ P(\text{from the U.S}) = \frac{\text{Number of people from the U.S}}{\text{Total number of people}} = \frac{34}{75} \][/tex]
Simplifying this fraction gives:
[tex]\[ P(\text{from the U.S}) \approx 0.4533 \][/tex]
### 2. Probability that someone has at least 2 children.
Let's first calculate the total number of people who have at least 2 children. This includes those with [tex]\(2\)[/tex] children and those with [tex]\(3\)[/tex] or more children.
From the table:
- Number of people with [tex]\(2\)[/tex] children: [tex]\(16\)[/tex]
- Number of people with [tex]\(3\)[/tex] or more children: [tex]\(19\)[/tex]
Summing these gives the total number of people with at least 2 children:
[tex]\[ 16 + 19 = 35 \][/tex]
The probability [tex]\(P(\text{at least 2 children})\)[/tex] can be calculated as:
[tex]\[ P(\text{at least 2 children}) = \frac{\text{Number of people with at least 2 children}}{\text{Total number of people}} = \frac{35}{75} \][/tex]
Simplifying this fraction gives:
[tex]\[ P(\text{at least 2 children}) \approx 0.4667 \][/tex]
### 3. Probability that someone is from the U.S. and has one child.
From the table, the number of people from the U.S. who have one child is [tex]\(15\)[/tex].
The probability [tex]\(P(\text{from the U.S. and has one child})\)[/tex] can be calculated as:
[tex]\[ P(\text{from the U.S. and has one child}) = \frac{\text{Number of U.S. people with one child}}{\text{Total number of people}} = \frac{15}{75} \][/tex]
Simplifying this fraction gives:
[tex]\[ P(\text{from the U.S. and has one child}) = 0.2 \][/tex]
### Summary of Probabilities:
1. The probability that someone is from the U.S. is approximately [tex]\(0.4533\)[/tex].
2. The probability that someone has at least 2 children is approximately [tex]\(0.4667\)[/tex].
3. The probability that someone is from the U.S. and has one child is [tex]\(0.2\)[/tex].
### 1. Probability that someone is from the U.S.
The total number of people surveyed is [tex]\(75\)[/tex]. Out of these, [tex]\(34\)[/tex] are from the U.S.
The probability [tex]\(P(\text{from the U.S})\)[/tex] can be calculated as:
[tex]\[ P(\text{from the U.S}) = \frac{\text{Number of people from the U.S}}{\text{Total number of people}} = \frac{34}{75} \][/tex]
Simplifying this fraction gives:
[tex]\[ P(\text{from the U.S}) \approx 0.4533 \][/tex]
### 2. Probability that someone has at least 2 children.
Let's first calculate the total number of people who have at least 2 children. This includes those with [tex]\(2\)[/tex] children and those with [tex]\(3\)[/tex] or more children.
From the table:
- Number of people with [tex]\(2\)[/tex] children: [tex]\(16\)[/tex]
- Number of people with [tex]\(3\)[/tex] or more children: [tex]\(19\)[/tex]
Summing these gives the total number of people with at least 2 children:
[tex]\[ 16 + 19 = 35 \][/tex]
The probability [tex]\(P(\text{at least 2 children})\)[/tex] can be calculated as:
[tex]\[ P(\text{at least 2 children}) = \frac{\text{Number of people with at least 2 children}}{\text{Total number of people}} = \frac{35}{75} \][/tex]
Simplifying this fraction gives:
[tex]\[ P(\text{at least 2 children}) \approx 0.4667 \][/tex]
### 3. Probability that someone is from the U.S. and has one child.
From the table, the number of people from the U.S. who have one child is [tex]\(15\)[/tex].
The probability [tex]\(P(\text{from the U.S. and has one child})\)[/tex] can be calculated as:
[tex]\[ P(\text{from the U.S. and has one child}) = \frac{\text{Number of U.S. people with one child}}{\text{Total number of people}} = \frac{15}{75} \][/tex]
Simplifying this fraction gives:
[tex]\[ P(\text{from the U.S. and has one child}) = 0.2 \][/tex]
### Summary of Probabilities:
1. The probability that someone is from the U.S. is approximately [tex]\(0.4533\)[/tex].
2. The probability that someone has at least 2 children is approximately [tex]\(0.4667\)[/tex].
3. The probability that someone is from the U.S. and has one child is [tex]\(0.2\)[/tex].
