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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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05 Jul 2018, 09:51
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45% (medium)

Question Stats:

61% (01:33) correct 39% (01:41) wrong based on 192 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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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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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.
Attachments

Probab sum.JPG [ 14.3 KiB | Viewed 1367 times ]

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

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02 Oct 2018, 21:48
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How can we assume that club D and club E are the only clubs that T can be a part of ?
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Re: A person is to be selected at random from the group T of people...  [#permalink]

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09 Oct 2018, 19:42
Is this indicative of a typical GMAT question? I've not come across a question in the OG where I have had to make such an assumption. (That D and E are the only clubs in T) Usually, it is mentioned in the question, which would make the answer 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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09 Oct 2018, 20:35
shaarang wrote:
Is this indicative of a typical GMAT question? I've not come across a question in the OG where I have had to make such an assumption. (That D and E are the only clubs in T) Usually, it is mentioned in the question, which would make the answer E.

Hey thanks for raising your query. The source of this question is Kaplan. I wouldn't say the wording is incorrect. Let me copy paste statement 1:-

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 1/4.

What do you infer from statement one?

Does your concern hold true any longer?
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Re: A person is to be selected at random from the group T of people...  [#permalink]

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27 Nov 2018, 09:29
CAMANISHPARMAR wrote:
shaarang wrote:
Is this indicative of a typical GMAT question? I've not come across a question in the OG where I have had to make such an assumption. (That D and E are the only clubs in T) Usually, it is mentioned in the question, which would make the answer E.

Hey thanks for raising your query. The source of this question is Kaplan. I wouldn't say the wording is incorrect. Let me copy paste statement 1:-

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 1/4.

What do you infer from statement one?

Does your concern hold true any longer?

I have a similar doubt. It is not considered the possibility that a person is member of club D and E at the same time, which would change the overall probability of being part of club D.
I think it should be explicitly stated that a person can't be part of club D and E at the same time, otherwise answer must be 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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27 Nov 2018, 22:26
fracheva wrote:
CAMANISHPARMAR wrote:
shaarang wrote:
Is this indicative of a typical GMAT question? I've not come across a question in the OG where I have had to make such an assumption. (That D and E are the only clubs in T) Usually, it is mentioned in the question, which would make the answer E.

Hey thanks for raising your query. The source of this question is Kaplan. I wouldn't say the wording is incorrect. Let me copy paste statement 1:-

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 1/4.

What do you infer from statement one?

Does your concern hold true any longer?

I have a similar doubt. It is not considered the possibility that a person is member of club D and E at the same time, which would change the overall probability of being part of club D.
I think it should be explicitly stated that a person can't be part of club D and E at the same time, otherwise answer must be E.

Hello

Lets take A= event that person is ONLY a member of club D
B = event that person is ONLY a member of club E
C= event that person is a member of BOTH clubs D/E
D= event that person is neither a member of club D nor a member of club E

We have to find the probability that person is a member of club E, which would include both events B&C. So the combined probability of B&C: P(B) + P(C).
And we know that P(A)+P(B)+P(C)+P(D) = 1 (total probability)

Statement 1 gives us probability of event D, P(D).
Statement 2 gives us probability of event A, P(A).
So combining, we can easily get P(B)+P(C).
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Re: A person is to be selected at random from the group T of people...  [#permalink]

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28 Nov 2018, 01:33
I have a similar doubt. It is not considered the possibility that a person is member of club D and E at the same time, which would change the overall probability of being part of club D.
I think it should be explicitly stated that a person can't be part of club D and E at the same time, otherwise answer must be E.[/quote]

Hello

Lets take A= event that person is ONLY a member of club D
B = event that person is ONLY a member of club E
C= event that person is a member of BOTH clubs D/E
D= event that person is neither a member of club D nor a member of club E

We have to find the probability that person is a member of club E, which would include both events B&C. So the combined probability of B&C: P(B) + P(C).
And we know that P(A)+P(B)+P(C)+P(D) = 1 (total probability)

Statement 1 gives us probability of event D, P(D).
Statement 2 gives us probability of event A, P(A).
So combining, we can easily get P(B)+P(C).[/quote]

Okay, now it's clear. Thank you so much, I was looking at the incorrect data.
Re: A person is to be selected at random from the group T of people...   [#permalink] 28 Nov 2018, 01:33
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