100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has failed in both the examinations?

(A) 1/5
(B) 1/7
(C) 5/7
(D) 5/6
(E) 6/7
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Hi saswata4s,

What is the source of this question? I ask because while it's meant to be an Overlapping Sets question, the answer choices are written in such a way that you can avoid almost of the "implied" math and still answer the question. Since there are exactly 100 students, the fraction that failed both Exams MUST be something "out of 100." Four of the five answer choices CANNOT be reduced from X/100, so they cannot be the correct answer. Only one of them can....

Final Answer:

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I used Venn Diagram to solve this question.
1st circle gives us 30 passed
2nd circle gives us 20 passed
inner part of both circles 1 and 2 give us 30 students. In total we have 80,but since total number of students is 100, we conclude that 20 students didn't pass the test. So, 20/100=1/5