Answer :
To determine the number of people who responded with a genre other than the ones listed, as well as to find the probabilities for a complete probability model, we need to follow these steps:
1. Total Number of Surveyed People: We are given that a total of 200 people were surveyed.
2. Number of People Responding to Each Genre:
- Adventure: 46 people
- Comedy: 36 people
- Mystery: 64 people
- Romance: 24 people
3. Calculate the Total Number of People Responding to the Listed Genres:
[tex]\[ 46 \text{ (Adventure)} + 36 \text{ (Comedy)} + 64 \text{ (Mystery)} + 24 \text{ (Romance)} = 170 \][/tex]
4. Calculate the Number of People Responding to Other Genres:
To find the number of people who responded with a genre other than the ones listed, subtract the sum of the people who chose the listed genres from the total number of surveyed people:
[tex]\[ 200 \text{ (total surveyed)} - 170 \text{ (sum of listed genres)} = 30 \text{ (other genres)} \][/tex]
5. Calculate Probabilities for Each Genre:
We need to find the probability for each genre by dividing the number of people for each genre by the total number of surveyed people.
- Probability of selecting Adventure:
[tex]\[ \frac{46}{200} = 0.23 \][/tex]
- Probability of selecting Comedy:
[tex]\[ \frac{36}{200} = 0.18 \][/tex]
- Probability of selecting Mystery:
[tex]\[ \frac{64}{200} = 0.32 \][/tex]
- Probability of selecting Romance:
[tex]\[ \frac{24}{200} = 0.12 \][/tex]
- Probability of selecting Other Genres:
[tex]\[ \frac{30}{200} = 0.15 \][/tex]
6. Summary of Probabilities:
The complete probability model for the responses is:
- Probability of Adventure: [tex]\(0.23\)[/tex]
- Probability of Comedy: [tex]\(0.18\)[/tex]
- Probability of Mystery: [tex]\(0.32\)[/tex]
- Probability of Romance: [tex]\(0.12\)[/tex]
- Probability of Other Genres: [tex]\(0.15\)[/tex]
Hence, the number of people who responded with a genre other than the listed ones is 30. The probabilities for a complete probability model for the responses are:
- Adventure: [tex]\(23\%\)[/tex] or [tex]\(0.23\)[/tex]
- Comedy: [tex]\(18\%\)[/tex] or [tex]\(0.18\)[/tex]
- Mystery: [tex]\(32\%\)[/tex] or [tex]\(0.32\)[/tex]
- Romance: [tex]\(12\%\)[/tex] or [tex]\(0.12\)[/tex]
- Other Genres: [tex]\(15\%\)[/tex] or [tex]\(0.15\)[/tex]
1. Total Number of Surveyed People: We are given that a total of 200 people were surveyed.
2. Number of People Responding to Each Genre:
- Adventure: 46 people
- Comedy: 36 people
- Mystery: 64 people
- Romance: 24 people
3. Calculate the Total Number of People Responding to the Listed Genres:
[tex]\[ 46 \text{ (Adventure)} + 36 \text{ (Comedy)} + 64 \text{ (Mystery)} + 24 \text{ (Romance)} = 170 \][/tex]
4. Calculate the Number of People Responding to Other Genres:
To find the number of people who responded with a genre other than the ones listed, subtract the sum of the people who chose the listed genres from the total number of surveyed people:
[tex]\[ 200 \text{ (total surveyed)} - 170 \text{ (sum of listed genres)} = 30 \text{ (other genres)} \][/tex]
5. Calculate Probabilities for Each Genre:
We need to find the probability for each genre by dividing the number of people for each genre by the total number of surveyed people.
- Probability of selecting Adventure:
[tex]\[ \frac{46}{200} = 0.23 \][/tex]
- Probability of selecting Comedy:
[tex]\[ \frac{36}{200} = 0.18 \][/tex]
- Probability of selecting Mystery:
[tex]\[ \frac{64}{200} = 0.32 \][/tex]
- Probability of selecting Romance:
[tex]\[ \frac{24}{200} = 0.12 \][/tex]
- Probability of selecting Other Genres:
[tex]\[ \frac{30}{200} = 0.15 \][/tex]
6. Summary of Probabilities:
The complete probability model for the responses is:
- Probability of Adventure: [tex]\(0.23\)[/tex]
- Probability of Comedy: [tex]\(0.18\)[/tex]
- Probability of Mystery: [tex]\(0.32\)[/tex]
- Probability of Romance: [tex]\(0.12\)[/tex]
- Probability of Other Genres: [tex]\(0.15\)[/tex]
Hence, the number of people who responded with a genre other than the listed ones is 30. The probabilities for a complete probability model for the responses are:
- Adventure: [tex]\(23\%\)[/tex] or [tex]\(0.23\)[/tex]
- Comedy: [tex]\(18\%\)[/tex] or [tex]\(0.18\)[/tex]
- Mystery: [tex]\(32\%\)[/tex] or [tex]\(0.32\)[/tex]
- Romance: [tex]\(12\%\)[/tex] or [tex]\(0.12\)[/tex]
- Other Genres: [tex]\(15\%\)[/tex] or [tex]\(0.15\)[/tex]
