Question
Seventh Grade Students
Instrument # of Students
Guitar 4
Bass 5
Drums 3
Keyboard 5
Eighth Grade Students
Instrument # of Students
Guitar 6
Bass 8
Drums 2
Keyboard 15
Based on these results, express the probability that a student chosen at random will play the guitar as a fraction
Answers
GPT-4o mini
To find the probability that a randomly chosen student plays the guitar, we first need to determine the total number of students and the number of students who play the guitar.
**Step 1: Calculate the total number of students.**
For seventh grade:
- Guitar: 4
- Bass: 5
- Drums: 3
- Keyboard: 5
Total for seventh grade = 4 + 5 + 3 + 5 = 17 students
For eighth grade:
- Guitar: 6
- Bass: 8
- Drums: 2
- Keyboard: 15
Total for eighth grade = 6 + 8 + 2 + 15 = 31 students
**Step 2: Add the total number of students from both grades.**
Total students = 17 (seventh grade) + 31 (eighth grade) = 48 students
**Step 3: Calculate the total number of students who play the guitar.**
Guitar players in both grades:
- Seventh grade: 4
- Eighth grade: 6
Total guitar players = 4 + 6 = 10 students
**Step 4: Calculate the probability of a student playing the guitar.**
Probability = (Number of Guitar Players) / (Total Number of Students)
Probability = 10 / 48
**Step 5: Simplify the fraction.**
To simplify \( \frac{10}{48} \), we can divide both numerator and denominator by their greatest common divisor, which is 2:
\[
\frac{10 \div 2}{48 \div 2} = \frac{5}{24}
\]
Thus, the probability that a student chosen at random will play the guitar is
\[
\frac{5}{24}.
\]
**Step 1: Calculate the total number of students.**
For seventh grade:
- Guitar: 4
- Bass: 5
- Drums: 3
- Keyboard: 5
Total for seventh grade = 4 + 5 + 3 + 5 = 17 students
For eighth grade:
- Guitar: 6
- Bass: 8
- Drums: 2
- Keyboard: 15
Total for eighth grade = 6 + 8 + 2 + 15 = 31 students
**Step 2: Add the total number of students from both grades.**
Total students = 17 (seventh grade) + 31 (eighth grade) = 48 students
**Step 3: Calculate the total number of students who play the guitar.**
Guitar players in both grades:
- Seventh grade: 4
- Eighth grade: 6
Total guitar players = 4 + 6 = 10 students
**Step 4: Calculate the probability of a student playing the guitar.**
Probability = (Number of Guitar Players) / (Total Number of Students)
Probability = 10 / 48
**Step 5: Simplify the fraction.**
To simplify \( \frac{10}{48} \), we can divide both numerator and denominator by their greatest common divisor, which is 2:
\[
\frac{10 \div 2}{48 \div 2} = \frac{5}{24}
\]
Thus, the probability that a student chosen at random will play the guitar is
\[
\frac{5}{24}.
\]