Question

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 plus 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 times Start Fraction 10 over 25 End Fraction

325
Start Fraction 3 over 25 End Fraction

Answer 1

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:
- \(A\) = the event that a student wants the option to keep studying online.
- \(B\) = the event that a student is a boy.

We want to find \(P(A \cup B)\), which can be calculated using the formula:

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

From the data provided:
- \(P(A) = \frac{13}{25}\) (number of students wanting to study online out of total students)
- \(P(B) = \frac{10}{25}\) (number of boys out of total students)
- \(P(A \cap B) = \frac{3}{25}\) (boys who want to study online)

Using the formula, we can substitute the values:

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

Thus, the mathematical sentence that can be used to calculate the probability is:

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

This matches with the response:

**Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction minus Start Fraction 3 over 25 End Fraction**.