To solve the problem, let's break it down into two main parts: calculating the number of people who responded with a genre other than those listed and determining the probabilities for a complete probability model for the responses.
### Step 1: Calculate the Number of People Who Responded with a Genre Other Than Those Listed
Given Data:
- Total number of people surveyed: 600
- Number of people who chose Adventure: 84
- Number of people who chose Comedy: 144
- Number of people who chose Mystery: 162
- Number of people who chose Romance: 132
First, we need to find the total number of people who chose the listed genres. We sum the numbers for each listed genre:
[tex]\[
84 + 144 + 162 + 132 = 522
\][/tex]
Next, we subtract this sum from the total number of people surveyed to find the number of people who responded with a genre other than the ones listed:
[tex]\[
600 - 522 = 78
\][/tex]
So, 78 people responded with a genre other than one of those listed.
### Step 2: Calculate the Probabilities for Each Genre
To find the probabilities for each genre, we divide the number of people who chose each genre by the total number of people surveyed (600).
#### Probability for Adventure:
[tex]\[
P(\text{Adventure}) = \frac{84}{600} = 0.14
\][/tex]
#### Probability for Comedy:
[tex]\[
P(\text{Comedy}) = \frac{144}{600} = 0.24
\][/tex]
#### Probability for Mystery:
[tex]\[
P(\text{Mystery}) = \frac{162}{600} = 0.27
\][/tex]
#### Probability for Romance:
[tex]\[
P(\text{Romance}) = \frac{132}{600} = 0.22
\][/tex]
#### Probability for Other Genres:
Given that 78 people chose genres other than those listed, we calculate this probability as follows:
[tex]\[
P(\text{Other Genres}) = \frac{78}{600} = 0.13
\][/tex]
### Conclusion
Of the people surveyed, 78 responded with a genre other than one of those listed. The probabilities for each genre in the complete probability model are:
- [tex]\( P(\text{Adventure}) = 0.14 \)[/tex]
- [tex]\( P(\text{Comedy}) = 0.24 \)[/tex]
- [tex]\( P(\text{Mystery}) = 0.27 \)[/tex]
- [tex]\( P(\text{Romance}) = 0.22 \)[/tex]
- [tex]\( P(\text{Other Genres}) = 0.13 \)[/tex]
