To find the probability of selecting a student who either wants the option to keep studying online or is a boy, we use the formula for the probability of the union of two events.
Let:
- A = the event that a student wants the option to keep studying online
- B = the event that a student is a boy
According to the table:
- Probability of A (wanting the option to keep studying online) = Number of students who want to study online / Total number of students = \( \frac{13}{25} \)
- Probability of B (being a boy) = Number of boys / Total number of students = \( \frac{10}{25} \)
- Probability of A and B (being both a boy and wanting to study online) = Number of boys who want the option to keep studying online / Total number of students = \( \frac{3}{25} \)
Using the formula for the union of two events: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Substituting the values: \[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Thus, the mathematical sentence that represents this calculation is: \[ \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Which matches with the response: Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction minus Start Fraction 3 over 25 End Fraction.
So, that is the correct option.