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.
Here's how you can break it down:
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Let A be the event that a student wants the option to keep studying online. The probability of A is \( P(A) = \frac{13}{25} \) because there are 13 students who want to keep studying online out of 25 total students.
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Let B be the event that a student is a boy. The probability of B is \( P(B) = \frac{10}{25} \) because there are 10 boys out of 25 total students.
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The intersection of events A and B, denoted as \( P(A \cap B) \), is the probability of selecting a student who is both a boy and wants to keep studying online. There are 3 boys who want the option, so \( P(A \cap B) = \frac{3}{25} \).
Using the inclusion-exclusion principle, the probability of selecting a student who wants to keep studying online or is a boy is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Substituting the values we calculated:
\[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Therefore, the mathematical sentence that can be used is:
\[ \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
So, the correct answer 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.