Use the table to answer the question. Studying Online This table presents the number of girls and boys who prefer or do not prefer studying online. Girls Boys Row total Want the option to keep studying online 10 3 13 Don’t want the option to keep studying online 5 7 12 Column total 15 10 25 Which mathematical sentence can be used to calculate the probability of selecting a student who wants the option to keep studying online or is a boy? (1 point) Responses 1325×1025 Start Fraction 13 over 25 End Fraction times Start Fraction 10 over 25 End Fraction 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 1325+1025 Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction 325 Start Fraction 3 over 25 End Fraction Skip to navigation

1 answer

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.