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100 students appeared for two examinations. 60 passed the first

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100 students appeared for two examinations. 60 passed the first [#permalink]

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New post 15 Feb 2017, 00:47
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Question Stats:

95% (01:02) correct 5% (01:24) wrong based on 55 sessions

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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
[Reveal] Spoiler: OA
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Re: 100 students appeared for two examinations. 60 passed the first [#permalink]

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New post 15 Feb 2017, 01:07
Lets calculate the number of students failed in each of the two exams.

A- 40 , B - 50. Now, the next thing to figure out is if these two events are dependent or independent events. These two events are independent events as the outcome of one does not influence the outcome of other. In this case the following formula hold true. p(A and B) = p(A) * p(B).

p(A) = 2/5 * 1/2 = 1/5.
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Re: 100 students appeared for two examinations. 60 passed the first [#permalink]

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New post 16 Feb 2017, 12:51
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....

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[Reveal] Spoiler:
A


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Re: 100 students appeared for two examinations. 60 passed the first [#permalink]

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New post 11 Mar 2017, 21:13
Can solve this quest by applying set theory
Let A= PPL who passed in 1st test =60
Let C= PPL who passed in 2nd test =50
Let B= overlap i.e. PPL who passed in both= 30
Then A+B=60
Therefore A=30
B+C= 50
Therefore C=20
A+B+C= 80
Remaining= 20 (PPL who did not pass at all)
=20/100= 1/5
Hence option A
Re: 100 students appeared for two examinations. 60 passed the first   [#permalink] 11 Mar 2017, 21:13
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100 students appeared for two examinations. 60 passed the first

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