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

1 answer

To calculate the probability of selecting a student who either wants the option to keep studying online or is a boy, we can use the principle of inclusion-exclusion.

Let:

  • A = the event of selecting a student who wants the option to keep studying online
  • B = the event of selecting a boy

From the table, we know:

  • \( P(A) \) (probability of A) is \( \frac{13}{25} \) (total students who want to study online)
  • \( P(B) \) (probability of B) is \( \frac{10}{25} \) (total boys)
  • \( P(A \cap B) \) (students who are both boys and want to study online) is \( \frac{3}{25} \)

Using the inclusion-exclusion principle:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Substituting in the values:

\[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]

Now looking at the options given, the mathematical sentence that represents this calculation is:

Option: \[ \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]

Thus, the correct response is:

1325+1025−325 \( \text{Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction minus Start Fraction 3 over 25 End Fraction} \)