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In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?
15%
20%
25%
35%
- Let P(E) be the probability of passing English = 80%.
- Let P(H) be the probability of passing Hindi = 70%.
- P(F) is the probability of failing both subjects = 15%.
- Use the formula for the union of two events:
P(E ? H) = P(E) + P(H) - P(E n H).
We know P(E ? H) = 100% - P(F) = 85%.
- So, 85% = 80% + 70% - P(E n H).
Solving, P(E n H) = 65%.
- Passing at least one subject is 85%, meaning 15% failed both.
- Students passing both English and Hindi are 65%.
- Therefore, students passing exactly one subject = 85% - 65% = 20% (failed in only one).
- Option 2: 20% is Correct.
By: Parvesh Mehta ProfileResourcesReport error
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