Use the table to answer the question.

Question

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

(1 point)
%

Answer 1

To find the probability that a student prefers German given that they are in the 11th grade, we will use the following formula for conditional probability:

\[ P(\text{German} \mid \text{11th grade}) = \frac{P(\text{German and 11th grade})}{P(\text{11th grade})} \]

From the table, we can see:

• The number of 11th graders who prefer German is 57.
• The total number of 11th graders is 189.

Now we can calculate:

\[ P(\text{German} \mid \text{11th grade}) = \frac{57}{189} \]

Now we calculate this fraction:

\[ P(\text{German} \mid \text{11th grade}) \approx 0.3016 \]

To convert this to a percentage, we multiply by 100:

\[ 0.3016 \times 100 \approx 30.16 \]

Rounding to the nearest percent, we find that:

\[ \text{Probability} \approx 30% \]

Thus, the final answer is 30%.