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Answer :
To solve the problem of determining which Venn diagram correctly represents the exam results in the class, follow these steps:
1. Identify the Given Information:
- There are a total of 30 students in the class.
- 20 students passed the chemistry exam.
- 14 students passed the physics exam.
- 6 students passed both the chemistry and physics exams.
2. Calculate the Number of Students Passing Only One Subject:
- Students passing only chemistry: Subtract the students who passed both exams from those who passed chemistry.
[tex]\[
\text{Passed only chemistry} = 20 - 6 = 14
\][/tex]
- Students passing only physics: Subtract the students who passed both exams from those who passed physics.
[tex]\[
\text{Passed only physics} = 14 - 6 = 8
\][/tex]
3. Calculate the Number of Students Not Passing Either Subject:
- To find the students who did not pass either subject, subtract the sum of students passing chemistry only, physics only, and both, from the total number of students.
[tex]\[
\text{Total students passing any subject} = 14 + 8 + 6 = 28
\][/tex]
[tex]\[
\text{Not passed either} = 30 - 28 = 2
\][/tex]
4. Venn Diagram Representation:
- The Venn diagram should show:
- 14 students in the region for only chemistry.
- 8 students in the region for only physics.
- 6 students in the overlapping region for both subjects.
Given these calculations, the option that matches this distribution is the correct Venn diagram, which is Venn diagram 1.
1. Identify the Given Information:
- There are a total of 30 students in the class.
- 20 students passed the chemistry exam.
- 14 students passed the physics exam.
- 6 students passed both the chemistry and physics exams.
2. Calculate the Number of Students Passing Only One Subject:
- Students passing only chemistry: Subtract the students who passed both exams from those who passed chemistry.
[tex]\[
\text{Passed only chemistry} = 20 - 6 = 14
\][/tex]
- Students passing only physics: Subtract the students who passed both exams from those who passed physics.
[tex]\[
\text{Passed only physics} = 14 - 6 = 8
\][/tex]
3. Calculate the Number of Students Not Passing Either Subject:
- To find the students who did not pass either subject, subtract the sum of students passing chemistry only, physics only, and both, from the total number of students.
[tex]\[
\text{Total students passing any subject} = 14 + 8 + 6 = 28
\][/tex]
[tex]\[
\text{Not passed either} = 30 - 28 = 2
\][/tex]
4. Venn Diagram Representation:
- The Venn diagram should show:
- 14 students in the region for only chemistry.
- 8 students in the region for only physics.
- 6 students in the overlapping region for both subjects.
Given these calculations, the option that matches this distribution is the correct Venn diagram, which is Venn diagram 1.
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