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:
- \( P(A) \) be the probability that a student wants the option to keep studying online.
- \( P(B) \) be the probability that a student is a boy.
- \( P(A \cap B) \) be the probability that a student is both wanting to study online and is a boy.
From the table:
- The total number of students is 25.
- The number of students who want the option to keep studying online is 13 (10 girls + 3 boys).
- The number of boys is 10.
We can calculate these probabilities:
- \( P(A) = \frac{13}{25} \)
- \( P(B) = \frac{10}{25} \)
- \( P(A \cap B) = \frac{3}{25} \) (the number of boys who want to study online)
Now, using the inclusion-exclusion principle: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substituting the values, we get: \[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Thus, the correct mathematical sentence that can be used to calculate this probability is: \[ \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
So, the correct response is: 1325 + 1025 - 325 Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction minus Start Fraction 3 over 25 End Fraction.