Answer :
To determine the joint relative frequency of being female and attending a drama movie, follow these detailed steps:
1. Understand the Joint Frequency:
- The joint frequency in this problem is the number of females who attended a drama movie. According to the table, this number is 191.
2. Determine the Total Number of Attendees:
- You need to find the total number of people who attended any movie, regardless of gender and movie type. From the table:
- Total males: [tex]\(105 \text{ (helian)} + 124 \text{ (drama)} = 229\)[/tex]
- Total females: [tex]\(9 \text{ (helian)} + 191 \text{ (drama)} = 200\)[/tex]
- Therefore, total attendees: [tex]\(229 \text{ (males)} + 200 \text{ (females)} = 429\)[/tex]
3. Calculate the Joint Relative Frequency:
- The joint relative frequency is found by dividing the joint frequency by the total number of attendees:
[tex]\[ \text{Joint Relative Frequency} = \frac{\text{Number of Females Who Attended Drama}}{\text{Total Number of Attendees}} = \frac{191}{429} \][/tex]
4. Identify the Correct Option:
- From the solution given, we know the correct division should be [tex]\( \frac{191}{429} \)[/tex].
- Among the provided options, the correct one is not directly described by any of the options given exactly as [tex]\( \frac{191}{429} \)[/tex]. However, contextually, the closest interpretation relates to dividing the number of females attending drama (191) by the total number of attendees (479), but note there seems to be a typographical mismatch.
Given the specific nature of provided frequency and the steps necessary to solve the problem, none of the provided answers directly align without correcting the total attendees to [tex]\(429\)[/tex].
Thus, strictly speaking, the solution demonstrates there might be a mistake in the options provided or in the table transcription.
1. Understand the Joint Frequency:
- The joint frequency in this problem is the number of females who attended a drama movie. According to the table, this number is 191.
2. Determine the Total Number of Attendees:
- You need to find the total number of people who attended any movie, regardless of gender and movie type. From the table:
- Total males: [tex]\(105 \text{ (helian)} + 124 \text{ (drama)} = 229\)[/tex]
- Total females: [tex]\(9 \text{ (helian)} + 191 \text{ (drama)} = 200\)[/tex]
- Therefore, total attendees: [tex]\(229 \text{ (males)} + 200 \text{ (females)} = 429\)[/tex]
3. Calculate the Joint Relative Frequency:
- The joint relative frequency is found by dividing the joint frequency by the total number of attendees:
[tex]\[ \text{Joint Relative Frequency} = \frac{\text{Number of Females Who Attended Drama}}{\text{Total Number of Attendees}} = \frac{191}{429} \][/tex]
4. Identify the Correct Option:
- From the solution given, we know the correct division should be [tex]\( \frac{191}{429} \)[/tex].
- Among the provided options, the correct one is not directly described by any of the options given exactly as [tex]\( \frac{191}{429} \)[/tex]. However, contextually, the closest interpretation relates to dividing the number of females attending drama (191) by the total number of attendees (479), but note there seems to be a typographical mismatch.
Given the specific nature of provided frequency and the steps necessary to solve the problem, none of the provided answers directly align without correcting the total attendees to [tex]\(429\)[/tex].
Thus, strictly speaking, the solution demonstrates there might be a mistake in the options provided or in the table transcription.
