To find out how many of the 200 additional students would be expected to like mathematics, we first need to determine the proportion of students who favored mathematics in the initial survey of 100 students.
From the results provided:
- Number of students who like Mathematics: 10
- Total number of students surveyed: 100
The proportion of students who like Mathematics is:
\[ \text{Proportion} = \frac{\text{Number of students who like Mathematics}}{\text{Total number of students}} = \frac{10}{100} = 0.1 \]
Now, if we are to survey an additional 200 students, we can multiply this proportion by the new total.
Expected number of students who like Mathematics among the 200 new students:
\[ \text{Expected number} = \text{Proportion} \times \text{Number of new students} = 0.1 \times 200 = 20 \]
Thus, we would expect 20 of the 200 new students to like mathematics.