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Use the table to answer the question.

This table displays the number of 10th and 11th-grade students who prefer either hip-hop or pop.
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 which music genre they prefer.

Using relative frequencies, which of the following is true?

(1 point)
Responses

If you are an 11th grader, you are more likely to prefer hip-hop.
If you are an 11th grader, you are more likely to prefer hip-hop.

If you are a 10th grader, you are more likely to prefer pop.
If you are a 10th grader, you are more likely to prefer pop.

If you like pop, you are more likely to be a 10th grader.
If you like pop, you are more likely to be a 10th grader.

If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.
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1 answer

To determine which statement is true based on the relative frequencies, let's calculate the probabilities for each scenario:

  1. If you are an 11th grader, you are more likely to prefer hip-hop.

    The number of 11th graders who prefer hip-hop is 98. The total number of 11th graders is 245. Thus, the probability of an 11th grader preferring hip-hop is: \[ P(\text{Hip-Hop | 11th}) = \frac{98}{245} \approx 0.4 \] The number of 11th graders who prefer pop is 147, so: \[ P(\text{Pop | 11th}) = \frac{147}{245} \approx 0.6 \] Thus, this statement is false.

  2. If you are a 10th grader, you are more likely to prefer pop.

    The number of 10th graders who prefer pop is 53. The total number of 10th graders is 165. Thus, the probability of a 10th grader preferring pop is: \[ P(\text{Pop | 10th}) = \frac{53}{165} \approx 0.32 \] The number of 10th graders who prefer hip-hop is 112, so: \[ P(\text{Hip-Hop | 10th}) = \frac{112}{165} \approx 0.68 \] Thus, this statement is false.

  3. If you like pop, you are more likely to be a 10th grader.

    The total number of students who prefer pop is 200. The number of 10th graders who prefer pop is 53. Thus, the probability of preferring pop for a 10th grader is: \[ P(\text{10th | Pop}) = \frac{53}{200} = 0.265 \] The number of 11th graders who prefer pop is 147, thus: \[ P(\text{11th | Pop}) = \frac{147}{200} = 0.735 \] Thus, this statement is false.

  4. If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.

    The total number of students who prefer hip-hop is 210. The number of 10th graders who prefer hip-hop is 112. Thus, the probability of preferring hip-hop for a 10th grader is: \[ P(\text{10th | Hip-Hop}) = \frac{112}{210} \approx 0.533 \] The number of 11th graders who prefer hip-hop is 98, thus: \[ P(\text{11th | Hip-Hop}) = \frac{98}{210} \approx 0.467 \] Since these probabilities (about 0.533 and 0.467) are close to each other, we can say that students who like hip-hop are almost equally likely to be from 10th or 11th grade. Thus, this statement is true.

In conclusion, the true statement is: If you like hip-hop, you are almost equally likely to be from 10th or 11th grade.