To find the probability that a female student selected at random plays field hockey or volleyball, we can use the principle of inclusion-exclusion.
Let:
- \( A \) be the set of female students who play field hockey.
- \( B \) be the set of female students who play volleyball.
We know:
- \( |A| = 98 \) (number of students who play field hockey)
- \( |B| = 62 \) (number of students who play volleyball)
- \( |A \cap B| = 40 \) (number of students who play both sports)
We want to find \( |A \cup B| \), which is the number of students who play either field hockey or volleyball. The formula for \( |A \cup B| \) is:
\[ |A \cup B| = |A| + |B| - |A \cap B| \]
Substituting the values we have:
\[ |A \cup B| = 98 + 62 - 40 = 120 \]
Now, the probability that a randomly selected female student plays either field hockey or volleyball is given by:
\[ P(A \cup B) = \frac{|A \cup B|}{\text{Total number of female students}} = \frac{120}{200} \]
We can simplify this fraction:
\[ \frac{120}{200} = \frac{12}{20} = \frac{3}{5} \]
Thus, the probability that a female student plays field hockey or volleyball is:
\[ \boxed{\frac{3}{5}} \]