To find the probability of selecting a student who either wants the option to keep studying online or is a boy, you can apply the principle of inclusion-exclusion.
Let's define:
- \( A \): the event that a student wants the option to keep studying online.
- \( B \): the event that a student is a boy.
From the table:
- \( P(A) = \frac{13}{25} \) (the probability of selecting a student who wants to study online)
- \( P(B) = \frac{10}{25} \) (the probability of selecting a boy)
- \( P(A \cap B) = \frac{3}{25} \) (the probability of selecting a student who wants to study online and is a boy)
The formula for the probability of either event occurring is: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Plugging in the numbers: \[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
This results in: \[ P(A \cup B) = \frac{13 + 10 - 3}{25} = \frac{20}{25} \]
Thus, the option that correctly represents this mathematical sentence is: \[ \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Looking at your provided options, the valid choice that corresponds to this is: \( \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \).