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Answer :
To determine which Venn diagram correctly represents the given information about the students' exam results, let's break down the problem step-by-step:
1. Total Students: There are 30 students in the class.
2. Chemistry Exam:
- Students who passed chemistry: 20
3. Physics Exam:
- Students who passed physics: 14
4. Both Exams:
- Students who passed both chemistry and physics: 6
Now, let's find out how many students passed only one of the exams:
5. Only Chemistry:
- To find the number of students who passed only the chemistry exam, subtract the students who passed both exams from those who passed chemistry:
[tex]\[
\text{Only Chemistry} = 20 - 6 = 14
\][/tex]
6. Only Physics:
- Similarly, for the physics exam, subtract those who passed both exams from those who passed physics:
[tex]\[
\text{Only Physics} = 14 - 6 = 8
\][/tex]
7. Passed Either Subject (At Least One Exam):
- The number of students who passed at least one of the exams (either chemistry or physics or both) can be calculated by adding those who passed only one of the exams and those who passed both:
[tex]\[
\text{Either Subject} = 14 + 8 + 6 = 28
\][/tex]
Given these calculations, pick the Venn diagram that shows:
- 14 students passing only chemistry.
- 8 students passing only physics.
- 6 students passing both chemistry and physics.
This scenario will match the Venn diagram only if the numbers align with this distribution. Use this breakdown to confirm with the Venn diagram options to select the correct one.
1. Total Students: There are 30 students in the class.
2. Chemistry Exam:
- Students who passed chemistry: 20
3. Physics Exam:
- Students who passed physics: 14
4. Both Exams:
- Students who passed both chemistry and physics: 6
Now, let's find out how many students passed only one of the exams:
5. Only Chemistry:
- To find the number of students who passed only the chemistry exam, subtract the students who passed both exams from those who passed chemistry:
[tex]\[
\text{Only Chemistry} = 20 - 6 = 14
\][/tex]
6. Only Physics:
- Similarly, for the physics exam, subtract those who passed both exams from those who passed physics:
[tex]\[
\text{Only Physics} = 14 - 6 = 8
\][/tex]
7. Passed Either Subject (At Least One Exam):
- The number of students who passed at least one of the exams (either chemistry or physics or both) can be calculated by adding those who passed only one of the exams and those who passed both:
[tex]\[
\text{Either Subject} = 14 + 8 + 6 = 28
\][/tex]
Given these calculations, pick the Venn diagram that shows:
- 14 students passing only chemistry.
- 8 students passing only physics.
- 6 students passing both chemistry and physics.
This scenario will match the Venn diagram only if the numbers align with this distribution. Use this breakdown to confirm with the Venn diagram options to select the correct one.
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