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

325
Start Fraction 3 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
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Answer 1

To determine 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, we need to identify two probabilities:

1. The probability of selecting a student who wants the option to keep studying online.
2. The probability of selecting a boy.

Since there is overlap (some boys may also want to keep studying online), we need to apply the principle of inclusion-exclusion to avoid double-counting.

Let's define these probabilities:

- Let \( P(A) \) be the probability that a student wants to keep studying online.
- Let \( P(B) \) be the probability that a student is a boy.
- Let \( P(A \cap B) \) be the probability that a student is both a boy and wants to keep studying online.

From the table:
- The total number of students is \( 25 \).
- The number of students who want to keep studying online (both girls and boys) is \( 13 \).
- The number of boys is \( 10 \).
- The number of boys who want to keep studying online is \( 3 \).

Now we calculate the probabilities:

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

Using the inclusion-exclusion principle:

\[
P(A \cup B) = P(A) + P(B) - P(A \cap B)
\]
\[
P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} = \frac{13 + 10 - 3}{25} = \frac{20}{25}
\]

This expression corresponds to the mathematical sentence:

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

Therefore, the correct response is:

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