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In a class 40% of the students enrolled for Math and 70% enrolled for Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enroll for either of the two subjects?
- a)5%
- b)15%
- c)0%
- d)25%
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
In a class 40% of the students enrolled for Math and 70% enrolled for ...
Understanding the Problem
To find the percentage of students who did not enroll in either Math or Economics, we can use the principle of inclusion-exclusion.
Given Data
- Percentage of students enrolled in Math = 40%
- Percentage of students enrolled in Economics = 70%
- Percentage of students enrolled in both subjects = 15%
Applying Inclusion-Exclusion Principle
We can calculate the percentage of students enrolled in at least one of the two subjects using the formula:
\[
\text{Percentage enrolled in either Math or Economics} = P(M) + P(E) - P(M \cap E)
\]
Where:
- \( P(M) \) = Percentage enrolled in Math = 40%
- \( P(E) \) = Percentage enrolled in Economics = 70%
- \( P(M \cap E) \) = Percentage enrolled in both = 15%
Calculation
Substituting the values:
\[
P(M \cup E) = 40\% + 70\% - 15\%
\]
\[
P(M \cup E) = 95\%
\]
Finding Students Not Enrolled in Either Subject
To find the percentage of students who did not enroll in either Math or Economics, we subtract the percentage enrolled in at least one subject from 100%:
\[
\text{Percentage not enrolled in either} = 100\% - P(M \cup E)
\]
\[
\text{Percentage not enrolled in either} = 100\% - 95\% = 5\%
\]
Conclusion
Therefore, the percentage of students who did not enroll for either Math or Economics is **5%**, which corresponds to option 'A'.
To find the percentage of students who did not enroll in either Math or Economics, we can use the principle of inclusion-exclusion.
Given Data
- Percentage of students enrolled in Math = 40%
- Percentage of students enrolled in Economics = 70%
- Percentage of students enrolled in both subjects = 15%
Applying Inclusion-Exclusion Principle
We can calculate the percentage of students enrolled in at least one of the two subjects using the formula:
\[
\text{Percentage enrolled in either Math or Economics} = P(M) + P(E) - P(M \cap E)
\]
Where:
- \( P(M) \) = Percentage enrolled in Math = 40%
- \( P(E) \) = Percentage enrolled in Economics = 70%
- \( P(M \cap E) \) = Percentage enrolled in both = 15%
Calculation
Substituting the values:
\[
P(M \cup E) = 40\% + 70\% - 15\%
\]
\[
P(M \cup E) = 95\%
\]
Finding Students Not Enrolled in Either Subject
To find the percentage of students who did not enroll in either Math or Economics, we subtract the percentage enrolled in at least one subject from 100%:
\[
\text{Percentage not enrolled in either} = 100\% - P(M \cup E)
\]
\[
\text{Percentage not enrolled in either} = 100\% - 95\% = 5\%
\]
Conclusion
Therefore, the percentage of students who did not enroll for either Math or Economics is **5%**, which corresponds to option 'A'.
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Community Answer
In a class 40% of the students enrolled for Math and 70% enrolled for ...
Objective: Percentage of students who enrolled for neither of the two subjects
Let A be the set of students who enrolled for Math.
Let B be the set of students who enrolled for Economics.
(A ∪ B) is the set of students who have enrolled for at least one of the two subjects.
And (A ∩ B) is the set of students who have enrolled for both Math and Economics.
Let A be the set of students who enrolled for Math.
Let B be the set of students who enrolled for Economics.
(A ∪ B) is the set of students who have enrolled for at least one of the two subjects.
And (A ∩ B) is the set of students who have enrolled for both Math and Economics.
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
In this question, all n(A), n(B), n(A ∪ B), and (A ∩ B) are expressed in percentage terms.
n(A ∪ B) = 40 + 70 - 15 = 95%
That is 95% of the students have enrolled for at least one of the two subjects Math or Economics.
Therefore, the balance (100 - 95)% = 5% of the students have not enrolled for either of the two subjects.
Choice A is the correct answer.
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