At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
Let's go through each part of the questions along with their detailed solutions step by step.
#### 1. What is the probability that someone is from the U.S?
- From the given data table:
- People from outside the U.S are [7, 10, 11, 13, 41].
- Total people are [15, 25, 16, 19, 75].
- Calculate the total number of people from outside the U.S: [tex]\(7 + 10 + 11 + 13 + 41 = 82\)[/tex].
- Calculate the total number of people: [tex]\(15 + 25 + 16 + 19 + 75 = 150\)[/tex].
- Calculate the total number of people from the U.S: [tex]\(150 - 82 = 68\)[/tex].
- Probability [tex]\(P(U.S)\)[/tex] is:
[tex]\[ P(U.S) = \frac{\text{Total people from the U.S}}{\text{Total people}} = \frac{68}{150} = 0.4533 \][/tex]
#### 2. What is the probability that someone has at least 2 children?
- Number of people with 2 or more children is: 16 (with 2 children) + 19 (with 3 children) + 75 (with 4 or more children)
- [tex]\(P(\text{At least 2 children})\)[/tex] is:
[tex]\[ P(\text{At least 2 children}) = \frac{16 + 19 + 75}{150} = \frac{110}{150} = 0.7333 \][/tex]
#### 3. What is the probability that someone is from the U.S and has one child?
- Number of people with 1 child: 25 (Total), out of which 10 are from outside the U.S, so 25 - 10 = 15 are from the U.S.
- Probability [tex]\(P(U.S \cap 1 \text{ child})\)[/tex] is:
[tex]\[ P(U.S \cap 1 \text{ child}) = \frac{15}{150} = 0.1 \][/tex]
#### 4. What is the probability that someone is from the U.S or has 0 children?
- Number of people with 0 children: 15 (Total), out of which 7 are from outside the U.S, so 15 - 7 = 8 are from the U.S.
- Number of people from the U.S: 68.
- People who are either from the U.S or have 0 children:
[tex]\[ \text{Total U.S} + \text{Total with 0 children} - \text{People from the U.S and with 0 children} \][/tex]
[tex]\[ 68 + 15 - 8 = 75 \][/tex]
- Probability [tex]\(P(U.S \cup 0 \text{ children})\)[/tex] is:
[tex]\[ P(U.S \cup 0 \text{ children}) = \frac{75}{150} = 0.5 \][/tex]
#### 5. Given that the person is from the U.S, what is the probability that they have 3 or more children?
- People with 3 or more children: 19 (Total) + 75 (Total) = 94.
- From outside the U.S: 13 (with 3 children) + 41 (with 4 or more children) = 54.
- From the U.S: [tex]\(94 - 54 = 40\)[/tex].
- Given the person is from U.S, the conditional probability [tex]\(P(3 \text{ or more children} | U.S)\)[/tex] is:
[tex]\[ P(3 \text{ or more children} | U.S) = \frac{40}{68} = 0.5882 \][/tex]
#### 6. Given that the person has 1 child, what is the probability that person is from the U.S?
- Number of individuals with 1 child in total: 25.
- From within the U.S: 15.
- Given the person has 1 child, the conditional probability [tex]\(P(U.S | 1 \text{ child})\)[/tex] is:
[tex]\[ P(U.S | 1 \text{ child}) = \frac{15}{25} = 0.6 \][/tex]
### Summary
- The probability that someone is from the U.S is [tex]\(0.4533\)[/tex].
- The probability that someone has at least 2 children is [tex]\(0.7333\)[/tex].
- The probability that someone is from the U.S and has 1 child is [tex]\(0.1\)[/tex].
- The probability that someone is from the U.S or has 0 children is [tex]\(0.5\)[/tex].
- Given that the person is from the U.S, the probability that they have 3 or more children is [tex]\(0.5882\)[/tex].
- Given that the person has 1 child, the probability that person is from the U.S is [tex]\(0.6\)[/tex].
#### 1. What is the probability that someone is from the U.S?
- From the given data table:
- People from outside the U.S are [7, 10, 11, 13, 41].
- Total people are [15, 25, 16, 19, 75].
- Calculate the total number of people from outside the U.S: [tex]\(7 + 10 + 11 + 13 + 41 = 82\)[/tex].
- Calculate the total number of people: [tex]\(15 + 25 + 16 + 19 + 75 = 150\)[/tex].
- Calculate the total number of people from the U.S: [tex]\(150 - 82 = 68\)[/tex].
- Probability [tex]\(P(U.S)\)[/tex] is:
[tex]\[ P(U.S) = \frac{\text{Total people from the U.S}}{\text{Total people}} = \frac{68}{150} = 0.4533 \][/tex]
#### 2. What is the probability that someone has at least 2 children?
- Number of people with 2 or more children is: 16 (with 2 children) + 19 (with 3 children) + 75 (with 4 or more children)
- [tex]\(P(\text{At least 2 children})\)[/tex] is:
[tex]\[ P(\text{At least 2 children}) = \frac{16 + 19 + 75}{150} = \frac{110}{150} = 0.7333 \][/tex]
#### 3. What is the probability that someone is from the U.S and has one child?
- Number of people with 1 child: 25 (Total), out of which 10 are from outside the U.S, so 25 - 10 = 15 are from the U.S.
- Probability [tex]\(P(U.S \cap 1 \text{ child})\)[/tex] is:
[tex]\[ P(U.S \cap 1 \text{ child}) = \frac{15}{150} = 0.1 \][/tex]
#### 4. What is the probability that someone is from the U.S or has 0 children?
- Number of people with 0 children: 15 (Total), out of which 7 are from outside the U.S, so 15 - 7 = 8 are from the U.S.
- Number of people from the U.S: 68.
- People who are either from the U.S or have 0 children:
[tex]\[ \text{Total U.S} + \text{Total with 0 children} - \text{People from the U.S and with 0 children} \][/tex]
[tex]\[ 68 + 15 - 8 = 75 \][/tex]
- Probability [tex]\(P(U.S \cup 0 \text{ children})\)[/tex] is:
[tex]\[ P(U.S \cup 0 \text{ children}) = \frac{75}{150} = 0.5 \][/tex]
#### 5. Given that the person is from the U.S, what is the probability that they have 3 or more children?
- People with 3 or more children: 19 (Total) + 75 (Total) = 94.
- From outside the U.S: 13 (with 3 children) + 41 (with 4 or more children) = 54.
- From the U.S: [tex]\(94 - 54 = 40\)[/tex].
- Given the person is from U.S, the conditional probability [tex]\(P(3 \text{ or more children} | U.S)\)[/tex] is:
[tex]\[ P(3 \text{ or more children} | U.S) = \frac{40}{68} = 0.5882 \][/tex]
#### 6. Given that the person has 1 child, what is the probability that person is from the U.S?
- Number of individuals with 1 child in total: 25.
- From within the U.S: 15.
- Given the person has 1 child, the conditional probability [tex]\(P(U.S | 1 \text{ child})\)[/tex] is:
[tex]\[ P(U.S | 1 \text{ child}) = \frac{15}{25} = 0.6 \][/tex]
### Summary
- The probability that someone is from the U.S is [tex]\(0.4533\)[/tex].
- The probability that someone has at least 2 children is [tex]\(0.7333\)[/tex].
- The probability that someone is from the U.S and has 1 child is [tex]\(0.1\)[/tex].
- The probability that someone is from the U.S or has 0 children is [tex]\(0.5\)[/tex].
- Given that the person is from the U.S, the probability that they have 3 or more children is [tex]\(0.5882\)[/tex].
- Given that the person has 1 child, the probability that person is from the U.S is [tex]\(0.6\)[/tex].
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
