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 times Start Fraction 10 over 25 End Fraction

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

325
Start Fraction 3 over 25 End Fraction
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Answer 1

To find the probability of selecting a student who wants the option of 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 have:
- P(A) = Probability of choosing a student who wants to study online = \( \frac{13}{25} \)
- P(B) = Probability of choosing a boy = \( \frac{10}{25} \)
- P(A and B) = Probability of choosing a boy who wants to study online = \( \frac{3}{25} \)

Using the formula for the probability of A or B:

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

This simplifies to:

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

So the correct mathematical sentence that can be used to calculate this probability is:

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

Therefore, the appropriate 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.