To find out how many of the additional 200 students would be expected to like mathematics, we first need to determine the percentage of the original 100 students who preferred mathematics.
From the data provided:
- Number of students who liked Mathematics = 10
- Total number of students surveyed = 100
Now, we can calculate the percentage of students who like Mathematics:
\[ \text{Percentage of students who like Mathematics} = \left(\frac{\text{Number of students who like Mathematics}}{\text{Total students}}\right) \times 100 = \left(\frac{10}{100}\right) \times 100 = 10% \]
Now, if 200 more students are surveyed, we can find the expected number of students who would like Mathematics:
\[ \text{Expected number liking Mathematics} = 10% \text{ of } 200 = 0.10 \times 200 = 20 \]
So, the expected number of students who would like Mathematics out of the additional 200 students is 20.