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Of the 700 members of a certain organization, 120 are lawyers. Two mem

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Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 16 Jul 2018, 21:02
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Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?

A. 0.5
B. 0.6
C. 0.7
D. 0.8
E. 0.9

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Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 16 Jul 2018, 21:45
Probability of selecting 2 lawyers

120/700* 120*700 =0.2(approx)

Now probability of neither of the members is a lawyer = 1- 0.2= 0.8 (approx)

Ans: D
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Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 16 Jul 2018, 22:39
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sunita123 wrote:
Probability of selecting 2 lawyers

120/700* 120*700 =0.2(approx)

Now probability of neither of the members is a lawyer = 1- 0.2= 0.8 (approx)

Ans: D


Hi..
this is not the correct way..
1-P( both are lawyers) = P that both are not lawyer, so it will include when 1 of them is a lawyer... so wrong

here we are looking for NEITHER is a lawyer, so both are NOT lawyer, so 580C2
P = \(\frac{580}{700}*\frac{579}{699}\)~\((\frac{580}{700})^2=(\frac{560+20}{700})^2=(0.8+0.03)^2=0.83^2=\) something more than 0.65 so answer 0.7
C
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Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 17 Jul 2018, 00:40
Bunuel wrote:
Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?

A. 0.5
B. 0.6
C. 0.7
D. 0.8
E. 0.9


P(neither lawyer)=\(\frac{Ways-of-selecting-both-non-Lawyers}{Ways-of-selecting-2-members-out--of-700-members}\)
=\(\frac{580C2}{700C2}\)
=0.68
0.68 can be approximated to 0.7.

Ans. (C)
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Re: Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 17 Jul 2018, 08:12
Bunuel wrote:
Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?

A. 0.5
B. 0.6
C. 0.7
D. 0.8
E. 0.9



Note : we are asked to determine the probability of members who are not lawyer.

Total case : 700C2

Probable event = (700 - 120 ) = 580C2

Probability = 580C2 / 700C2

= 0.68 ~ 0.7.

The best answer is C.
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Re: Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 17 Jul 2018, 21:50
Bunuel wrote:
Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?

A. 0.5
B. 0.6
C. 0.7
D. 0.8
E. 0.9


# of non lawyers = 700 - 120 = 580

Probability of selecting 2 non lawyers = (580/700)*(579/699) =~ (580/700)*(580/700) =0.6889 =~0.7

Answer C.


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Re: Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 19 Jul 2018, 17:04
1
Bunuel wrote:
Of the 700 members of a certain organization, 120 are lawyers. Two members of the organization will be selected at random. Which of the following is closest to the probability that neither of the members selected will be a lawyer?

A. 0.5
B. 0.6
C. 0.7
D. 0.8
E. 0.9


Since 580 are not lawyers, the probability of selecting two members, neither of whom are lawyers, is:

580/700 x 579/699

Notice that the second fraction is approximately 580/700, so we can approximate the probability as:

580/700 x 580/700 = 58/70 x 58/70 = 29/35 x 29/35 ≈ 30/35 x 30/35 = 6/7 x 6/7 = 36/49 ≈ 36/50 = 0.72
Of the numbers in the given choices, the closest to this is 0.7.

Answer: C
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Re: Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 02 Aug 2018, 02:12
sunita123 wrote:
Probability of selecting 2 lawyers

120/700* 120*700 =0.2(approx) <----- The multiplication is wrong. It will be 0.02 instead of 0.2

Now probability of neither of the members is a lawyer = 1- 0.2= 0.8 (approx)

Ans: D
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Re: Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 02 Aug 2018, 02:18
chetan2u wrote:
sunita123 wrote:
Probability of selecting 2 lawyers

120/700* 120*700 =0.2(approx)

Now probability of neither of the members is a lawyer = 1- 0.2= 0.8 (approx)

Ans: D


Hi..
this is not the correct way..
1-P( both are lawyers) = P that both are not lawyer, so it will include when 1 of them is a lawyer... so wrong

here we are looking for NEITHER is a lawyer, so both are NOT lawyer, so 580C2
P = \(\frac{580}{700}*\frac{579}{699}\)~\((\frac{580}{700})^2=(\frac{560+20}{700})^2=(0.8+0.03)^2=0.83^2=\) something more than 0.65 so answer 0.7
C



Sir,
Can you please help me in removing my concept gap. I tried to solve it in a very layman way.
* Select one person from 580 and second person from 579
=(1/580) x (1/579) :(
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Re: Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 02 Aug 2018, 10:06
1
tatz wrote:
chetan2u wrote:
sunita123 wrote:
Probability of selecting 2 lawyers

120/700* 120*700 =0.2(approx)

Now probability of neither of the members is a lawyer = 1- 0.2= 0.8 (approx)

Ans: D


Hi..
this is not the correct way..
1-P( both are lawyers) = P that both are not lawyer, so it will include when 1 of them is a lawyer... so wrong

here we are looking for NEITHER is a lawyer, so both are NOT lawyer, so 580C2
P = \(\frac{580}{700}*\frac{579}{699}\)~\((\frac{580}{700})^2=(\frac{560+20}{700})^2=(0.8+0.03)^2=0.83^2=\) something more than 0.65 so answer 0.7
C



Sir,
Can you please help me in removing my concept gap. I tried to solve it in a very layman way.
* Select one person from 580 and second person from 579
=(1/580) x (1/579) :(

This is not correct way to solve this question.
Since you mention "select one person from 580 ...", you can think it this way:

ways of selecting 1st member from 580 members who are not lawyers = 580C1 = 580
ways of selecting 2nd member from 579 members who are not lawyers = 579C1 = 579
Total possible ways = 700 (ways of selecting 1st member from 700 members) * 699 (ways of selecting 2nd member from the rest 699 members)

Therefore, Probability of selecting both members who are not lawyer = (580*579) / (700*699) = 0.7 (approx.)
Answer: C.

Hope it helps.
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Re: Of the 700 members of a certain organization, 120 are lawyers. Two mem  [#permalink]

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New post 02 Aug 2018, 13:29
Thanks Izzyjust5.. it made things clear ..
Probably selecting 1 object out of 580 objects (1/580) will be correct only when all objects are same/similar like all are red balls or green pens.
In case all objects are unique, we need to use combinations.. "r objects can be selected from a set of n unique objects in nCr ways.."
Re: Of the 700 members of a certain organization, 120 are lawyers. Two mem &nbs [#permalink] 02 Aug 2018, 13:29
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