Students were surveyed about their favorite language class. Their responses are recorded in the table. According to the table, what is the probability that a student will prefer German, given that they are in the 11th grade? Round your answer to the nearest percent.

Question

(1 point)

French

German Spanish TOTAL

9th
58
47
63
168
10th
70
64
44
178
11th
67
57
65
189
TOTAL
195
168
172
535

Answer 1

To find the probability that a student will prefer German given that they are in the 11th grade, we will follow these steps:

1. Identify the number of students in the 11th grade who prefer German.
   From the table, 57 students in the 11th grade prefer German.

2. Identify the total number of students in the 11th grade.
   From the table, the total number of students in the 11th grade is 189.

3. Calculate the probability.
   The probability \( P(\text{German} \mid \text{11th grade}) \) is given by the formula: \[ P(\text{German} \mid \text{11th grade}) = \frac{\text{Number of students preferring German in 11th grade}}{\text{Total number of students in 11th grade}} = \frac{57}{189}. \]

4. Perform the calculation. \[ \frac{57}{189} \approx 0.3016. \]

5. Convert to a percentage and round.
   \[ 0.3016 \times 100 \approx 30.16%. \] Rounding to the nearest percent gives approximately 30%.

Therefore, the probability that a student in the 11th grade will prefer German is 30%.