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30 Sep 2024, 01:30
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C
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Difficulty:
45%
(medium)
Question Stats:
68% (01:48) correct
32%
(01:43)
wrong
based on 225
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A person is to be selected at random from the group T of people. What is the probability that the person selected is a member of club E?
(1) The probability that a person selected at random from group T is not a member of club D and is not a member of club E is \(\frac{1}{4}\).
(2) The probability that a person selected at random from group T is a member of club D and not a member of club E is \(\frac{5}{12}\).
(1) The probability that a person selected at random from group T is not a member of club D and is not a member of club E is \(\frac{1}{4}\).
(2) The probability that a person selected at random from group T is a member of club D and not a member of club E is \(\frac{5}{12}\).
This is a Data Sufficiency Butler Question
Check the links to other Butler Projects:
Check the links to other Butler Projects:
- Data Sufficiency Butler
- Problem Solving Butler
- Sentence Correction Butler
- Reading Comprehension Butler
- Integrated Reasoning Butler
30 Sep 2024, 07:43
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Bunuel
To find - E = probability that the person selected is a member of club E.
1st - The probability that a person selected at random from group T is not a member of club D and is not a member of club E is \(\frac{1}{4}\).
\(D'∩E' = \frac{1}{4}\) Nothing else so not sufficient.
2nd - The probability that a person selected at random from group T is a member of club D and not a member of club E is \(\frac{5}{12}\).
This value gives us the value for Only D. i.e. \(D - D∩E = \frac{5}{12}\) But still this is not sufficient to calculate E.
Now lets combine both,
As we know from 1st statement, \(D'∩E' = \frac{1}{4}\)
But, \(D'∩E' = (DUE)'\) (Property of sets)
Therefore, \((DUE)' = \frac{1}{4}\)
But \((DUE)' + DUE = 1\) (Property of sets)
Therefore, \(DUE = 1 - \frac{1}{4} = \frac{3}{4}\)
and \(DUE = D + E - D∩E\)
and from statement 2 we know \(D - D∩E = \frac{5}{12}\)
Therefore \(\frac{3}{4} = \frac{5}{12} + E\)
From here \(E = \frac{1}{3}\)
Sufficient.
Answer is C.
