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+1025−325
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
1325+1025
Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction
1325×1025
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+1025−325
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
1325+1025
Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction
1325×1025
Answers
GPT-4o mini
To calculate the probability of selecting a student who wants the option to keep studying online or is a boy, we can use the formula for the probability of the union of two events, which is given by:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
where:
- \( P(A) \) is the probability of selecting a student who wants the option to keep studying online.
- \( P(B) \) is the probability of selecting a boy.
- \( P(A \cap B) \) is the probability of selecting a student who wants to study online and is also a boy.
From the table:
- The total number of students is 25.
- The number of students who want to keep studying online is 13.
- The number of boys is 10.
- The number of boys who want to keep studying online is 3.
Now, we can express these probabilities as fractions:
- \( P(A) = \frac{13}{25} \)
- \( P(B) = \frac{10}{25} \)
- \( P(A \cap B) = \frac{3}{25} \)
Plugging these values into the formula, we have:
\[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Thus, the correct mathematical sentence that can be used to calculate the probability of selecting a student who wants the option to keep studying online or is a boy is:
**Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction minus Start Fraction 3 over 25 End Fraction**
This corresponds to 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**.
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
where:
- \( P(A) \) is the probability of selecting a student who wants the option to keep studying online.
- \( P(B) \) is the probability of selecting a boy.
- \( P(A \cap B) \) is the probability of selecting a student who wants to study online and is also a boy.
From the table:
- The total number of students is 25.
- The number of students who want to keep studying online is 13.
- The number of boys is 10.
- The number of boys who want to keep studying online is 3.
Now, we can express these probabilities as fractions:
- \( P(A) = \frac{13}{25} \)
- \( P(B) = \frac{10}{25} \)
- \( P(A \cap B) = \frac{3}{25} \)
Plugging these values into the formula, we have:
\[ P(A \cup B) = \frac{13}{25} + \frac{10}{25} - \frac{3}{25} \]
Thus, the correct mathematical sentence that can be used to calculate the probability of selecting a student who wants the option to keep studying online or is a boy is:
**Start Fraction 13 over 25 End Fraction plus Start Fraction 10 over 25 End Fraction minus Start Fraction 3 over 25 End Fraction**
This corresponds to 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**.