Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To solve the problem of finding the probabilities associated with the given data table, let's carefully analyze the information provided. Here's a structured approach to the solution:
1. Total number of respondents: According to the table, the total number of respondents in each category is given in the last row.
- [tex]$Total = 80 + 170 + 250 = 500$[/tex]
2. Probability of a randomly selected person identifying as Liberal:
- The number of respondents identifying as Liberal from the given data:
- [tex]$Liberal = 80$[/tex]
- Therefore, the probability of a randomly selected person identifying as Liberal is:
[tex]\[ P(\text{Liberal}) = \frac{\text{Number of Liberals}}{\text{Total number of respondents}} = \frac{80}{500} \][/tex]
- Simplifying the fraction:
[tex]\[ P(\text{Liberal}) = \frac{80}{500} = \frac{8}{50} = \frac{4}{25} \][/tex]
3. Probability of a randomly selected person identifying as Liberal and holding a College Degree:
- The number of respondents identifying as Liberal and holding a College Degree should be provided directly or computed by dividing:
- [tex]$Liberal \land \text{College Degree} = 42$[/tex] (as per problem statement, not from the given data)
- Therefore, the probability is:
[tex]\[ P(\text{Liberal} \land \text{College Degree}) = \frac{\text{Number of Liberals with College Degree}}{\text{Total number of respondents}} = \frac{42}{500} \][/tex]
- Simplifying the fraction:
[tex]\[ P(\text{Liberal} \land \text{College Degree}) = \frac{42}{500} = \frac{21}{250} \][/tex]
4. Probability of a randomly selected person identifying as Liberal, or identifying as Mixed, or identifying as Conservative:
- Since these are all the categories provided, and they cover the complete set of respondents, we can infer:
[tex]\[ P(\text{Liberal} \lor \text{Mixed} \lor \text{Conservative}) = 1 \][/tex]
With this detailed explanation, we now have matching probabilities.
- Probability of a randomly selected person identifying as Liberal: [tex]$\frac{4}{25}$[/tex]
- Probability of a randomly selected person identifying as Liberal and holding a College Degree: [tex]$\frac{42}{250}$[/tex]
1. Total number of respondents: According to the table, the total number of respondents in each category is given in the last row.
- [tex]$Total = 80 + 170 + 250 = 500$[/tex]
2. Probability of a randomly selected person identifying as Liberal:
- The number of respondents identifying as Liberal from the given data:
- [tex]$Liberal = 80$[/tex]
- Therefore, the probability of a randomly selected person identifying as Liberal is:
[tex]\[ P(\text{Liberal}) = \frac{\text{Number of Liberals}}{\text{Total number of respondents}} = \frac{80}{500} \][/tex]
- Simplifying the fraction:
[tex]\[ P(\text{Liberal}) = \frac{80}{500} = \frac{8}{50} = \frac{4}{25} \][/tex]
3. Probability of a randomly selected person identifying as Liberal and holding a College Degree:
- The number of respondents identifying as Liberal and holding a College Degree should be provided directly or computed by dividing:
- [tex]$Liberal \land \text{College Degree} = 42$[/tex] (as per problem statement, not from the given data)
- Therefore, the probability is:
[tex]\[ P(\text{Liberal} \land \text{College Degree}) = \frac{\text{Number of Liberals with College Degree}}{\text{Total number of respondents}} = \frac{42}{500} \][/tex]
- Simplifying the fraction:
[tex]\[ P(\text{Liberal} \land \text{College Degree}) = \frac{42}{500} = \frac{21}{250} \][/tex]
4. Probability of a randomly selected person identifying as Liberal, or identifying as Mixed, or identifying as Conservative:
- Since these are all the categories provided, and they cover the complete set of respondents, we can infer:
[tex]\[ P(\text{Liberal} \lor \text{Mixed} \lor \text{Conservative}) = 1 \][/tex]
With this detailed explanation, we now have matching probabilities.
- Probability of a randomly selected person identifying as Liberal: [tex]$\frac{4}{25}$[/tex]
- Probability of a randomly selected person identifying as Liberal and holding a College Degree: [tex]$\frac{42}{250}$[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.