To find the probability of selecting a student who wants the option to keep studying online or is a boy, we can use the principle of inclusion-exclusion.
Let:
- \( P(A) \): Probability that a student wants to keep studying online.
- \( P(B) \): Probability that a student is a boy.
- \( P(A \cap B) \): Probability that a student is both wanting to keep studying online and is a boy.
From the table:
- Total number of students = 25
- Number of students that want the option to keep studying online \( (A) = 13 \)
- Number of boys \( (B) = 10 \)
- Number of students that want to study online and are boys \( (A \cap B) = 3 \)
The probabilities are:
- \( P(A) = \frac{13}{25} \)
- \( P(B) = \frac{10}{25} \)
- \( P(A \cap B) = \frac{3}{25} \)
Using the inclusion-exclusion principle, the probability that a student either wants to study online or is a boy is calculated as follows:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Substituting in the values we have:
\[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} = \frac{13 + 10 - 3}{25} = \frac{20}{25} \]
So the mathematical sentence that could be used is:
\[ \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
This corresponds to the option:
\( \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \).