Use the table to answer the question.

| | Hip-Hop | Pop | Totals |
|----------|---------|-----|--------|
| 10th Grade | 112 | 53 | 165 |
| 11th Grade | 98 | 147 | 245 |
| Total | 210 | 200 | 410 |

Examine the data from a survey of 10th and 11th graders about their preferred music genre.

Using relative frequencies, which of the following is true?

A. If you are an 11th grader, you are more likely to prefer hip-hop.
B. If you like pop, you are more likely to be a 10th grader.
C. If you are a 10th grader, you are more likely to prefer pop.
D. If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.



Answer :

Let's interpret and analyze the data provided in the table and address each of the given statements using relative frequencies and probabilities.

Table Summary:
- 10th Grade:
- Hip-Hop: 112
- Pop: 53
- Total Students: 165
- 11th Grade:
- Hip-Hop: 98
- Pop: 147
- Total Students: 245
- Overall:
- Hip-Hop Total: 210
- Pop Total: 200
- Total Students: 410

### Step-by-Step Analysis:

1. Probability if you are an 11th grader and prefer hip-hop:
- Number of 11th graders who like Hip-Hop: 98
- Total number of 11th graders: 245
- Relative frequency [tex]\( P(\text{Hip-Hop} | \text{11th Grade}) \)[/tex]:
[tex]\[ \frac{98}{245} = 0.4 = 40\% \][/tex]
- Therefore, the probability is 40%.

2. Probability if you like pop, you are more likely to be a 10th grader:
- Number of 10th graders who like Pop: 53
- Total number of students who like Pop: 200
- Relative frequency [tex]\( P(\text{10th Grade} | \text{Pop}) \)[/tex]:
[tex]\[ \frac{53}{200} = 0.265 = 26.5\% \][/tex]
- Therefore, the probability is 26.5%.

3. Probability if you are a 10th grader, you are more likely to prefer pop:
- Number of 10th graders who like Pop: 53
- Total number of 10th graders: 165
- Relative frequency [tex]\( P(\text{Pop} | \text{10th Grade}) \)[/tex]:
[tex]\[ \frac{53}{165} = 0.3212 \approx 32.1\% \][/tex]
- Therefore, the probability is approximately 32.1%.

4. Probability if you like hip-hop, you are almost equally likely to be from 10th or 11th grade:
- Number of 10th graders who like Hip-Hop: 112
- Number of 11th graders who like Hip-Hop: 98
- Total number of students who like Hip-Hop: 210
- Relative frequency [tex]\( P(\text{10th Grade} | \text{Hip-Hop}) \)[/tex]:
[tex]\[ \frac{112}{210} = 0.5333 \approx 53.3\% \][/tex]
- Relative frequency [tex]\( P(\text{11th Grade} | \text{Hip-Hop}) \)[/tex]:
[tex]\[ \frac{98}{210} = 0.4667 \approx 46.7\% \][/tex]
- These probabilities are quite close (53.3% vs. 46.7%), indicating that you are almost equally likely to be from either the 10th or 11th grade if you like Hip-Hop.

### Conclusion:
Based on the relative frequencies calculated:

- The first statement "If you are an 11th grader, you are more likely to prefer hip-hop" is true with a probability of 40%.
- The second statement "If you like pop, you are more likely to be a 10th grader" is false with a probability of only 26.5%.
- The third statement "If you are a 10th grader, you are more likely to prefer pop" is false with a probability of 32.1%, which is lower than 50%.
- The fourth statement "If you like hip-hop, you are almost equally likely to be from 10th or 11th grade" is true, with probabilities 53.3% and 46.7%, respectively.

Thus, the true statements based on the data and relative frequency analysis are:
- "If you are an 11th grader, you are more likely to prefer hip-hop".
- "If you like hip-hop, you are almost equally likely to be from 10th or 11th grade".