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A person is to be selected at random from the group T of people...

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A person is to be selected at random from the group T of people...  [#permalink]

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New post 05 Jul 2018, 09:51
2
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A
B
C
D
E

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  45% (medium)

Question Stats:

53% (01:32) correct 47% (01:56) wrong based on 32 sessions

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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 \(\frac{5}{12}\).

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Re: A person is to be selected at random from the group T of people...  [#permalink]

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New post 05 Jul 2018, 10:40
CAMANISHPARMAR wrote:
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 \(\frac{5}{12}\).



Individually each statement cannot be sufficient as it talks of club D and club E both..


Combined..
Prob that person selected is neither from D nor from E is 1/4, so prob that the person is from one of D or E is 1-1/4=3/4
Statement II tells us D but not E is 5/12
Ans 3/4-5/12=4/12=1/3
Sufficient

If this were a PS problem...
Take total strength 12...
3/4 belong to D or E or Both so 12*3/4=9
But only D is 5/12, so 5 on only D
Remaining 9-5=4 in E
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Re: A person is to be selected at random from the group T of people...  [#permalink]

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New post 05 Jul 2018, 11:29
CAMANISHPARMAR wrote:
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 \(\frac{5}{12}\).


Refer the affixed Venn diagram,
Question stem, probability that the person selected is a member of club E or a+c=?

statement-1:-
Given,he 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 \(\frac{1}{4}\)
Or,\(n=\frac{1}{4}\)
we have, a+b+c+n=T
Or, (\(a+c)=T-n-b=1-\frac{1}{4}-b=\frac{3}{4}-b\)---------------(1) (T=1 because total probability is always 1)
Since 'b' is not provided, we can't determine a+c.
So, insufficient.
statement-2:-
Given, 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 \(\frac{5}{12}\)
Or, \(b=\frac{5}{12}\)--------------(2)
Since, we don't have info on "n", we can't determine a+c.
So, insufficient.

Now combining, from (1) & (2) we have \(a+c\)=\(\frac{3}{4}\)-\(\frac{5}{12}\)=\(\frac{1}{3}\)

Sufficient.

Ans. (C)
Hope it helps.
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Re: A person is to be selected at random from the group T of people... &nbs [#permalink] 05 Jul 2018, 11:29
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