To find the probability of selecting a student who either wants the option to keep studying online or is a boy, we can use the principle of inclusion-exclusion.
Let's define:
- A: the event of selecting a student who wants the option to keep studying online,
- B: the event of selecting a student who is a boy.
From the table:
- The probability of event A (students who want the option to keep studying online) is \( P(A) = \frac{13}{25} \).
- The probability of event B (students who are boys) is \( P(B) = \frac{10}{25} \).
- The probability of both events occurring (boys who want to keep studying online) is \( P(A \cap B) = \frac{3}{25} \).
Using the inclusion-exclusion principle to find \( P(A \cup B) \):
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Substituting the probabilities:
\[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Now translating this into the correct mathematical sentence gives:
\[ \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Thus, the answer is:
Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction minus Start Fraction 3 over 25 End Fraction.