In an examination, 42% of the students failed Mathematics and 52% failed…
2022
In an examination, 42% of the students failed Mathematics and 52% failed Science. If 17% failed both subjects, what percentage passed both subjects?
Answer: A. 23% — ConceptFor two sets A and B, inclusion–exclusion gives P(A ∪ B) = P(A) + P(B) − P(A ∩ B). The people outside A ∪ B form its complement, so their percentage is…
- A.
23%
- B.
25%
- C.
27%
- D.
30%
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
For two sets A and B, inclusion–exclusion gives P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
The people outside A ∪ B form its complement, so their percentage is 100% − P(A ∪ B).
Application
Let A be the students who failed Mathematics and B be the students who failed Science.
Students who failed at least one subject = 42% + 52% − 17% = 77%.
Students who passed both subjects are the complement of those who failed at least one subject.
Therefore, students who passed both = 100% − 77% = 23%.
Cross-check
The four disjoint groups can be checked as: only Mathematics fail = 42% − 17% = 25%, only Science fail = 52% − 17% = 35%, both fail = 17%, and pass both = 23%. Their total is 25% + 35% + 17% + 23% = 100%.
Hence, 23% of the students passed both subjects.