To calculate 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:
- A = the event of selecting a student who wants the option to keep studying online
- B = the event of selecting a boy
From the table, we know:
- \( P(A) \) (probability of A) is \( \frac{13}{25} \) (total students who want to study online)
- \( P(B) \) (probability of B) is \( \frac{10}{25} \) (total boys)
- \( P(A \cap B) \) (students who are both boys and want to study online) is \( \frac{3}{25} \)
Using the inclusion-exclusion principle:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Substituting in the values:
\[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Now looking at the options given, the mathematical sentence that represents this calculation is:
Option: \[ \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Thus, the correct response is:
1325+1025−325 \( \text{Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction minus Start Fraction 3 over 25 End Fraction} \)