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From a class of 12 students, two students will be randomly chosen simu

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From a class of 12 students, two students will be randomly chosen simu  [#permalink]

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30 Jan 2018, 07:20
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85% (hard)

Question Stats:

38% (02:10) correct 62% (02:11) wrong based on 94 sessions

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From a class of 12 students, two students will be randomly chosen simultaneously. If g is the number of girls in the class, what is the value of g?

(1) The probability that two girls will be chosen together is 1/11.
(2) The probability that one boy and one girl will be chosen is 16/33.

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From a class of 12 students, two students will be randomly chosen simu  [#permalink]

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30 Jan 2018, 08:38
1
Bunuel wrote:
From a class of 12 students, two students will be randomly chosen simultaneously. If g is the number of girls in the class, what is the value of g?

(1) The probability that two girls will be chosen together is 1/11.
(2) The probability that one boy and one girl will be chosen is 16/33.

Let the number of girl be g, then the number of boys =12-g...

(1) The probability that two girls will be chosen together is 1/11.
P of first as girl = $$\frac{g}{12}$$..
P of second as girl = $$\frac{(g-1)}{11}$$..
Combined prob = $$\frac{g}{12} * \frac{(g-1)}{11}=\frac{1}{11}$$...
$$g (g-1)=12=4*3$$...
So g is 4
Sufficient..

2) The probability that one boy and one girl will be chosen is 16/33..
Whatever Ans we get can be of boys or girls..
So insufficient..
$$\frac{(12-g)}{12} *\frac{g}{11} * 2=\frac{16}{33}....... (12-g)g=32...$$
So g can be 8 or 4..
Insuff

A
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Re: From a class of 12 students, two students will be randomly chosen simu  [#permalink]

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30 Jan 2018, 20:57
Assume the number of girls be g

(1) Probability of two girls chosen together is 1/11.
(gC2)/12C2=1/11
or g*(g-1)/(12*11) =1/11
or g*(g-1)=12=4*3
Hence, g is 4
Considering only 1 is Sufficient.

2) Probability of one boy and one girl chosen is 16/33..
gC1*(12-g)C1/12C2) = 16/33
Solving, we get : g*(g-1) = 32
So g can be 8 or 4..
Hence, Insufficient.

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Re: From a class of 12 students, two students will be randomly chosen simu  [#permalink]

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31 Jan 2018, 09:36
What is OA? M confused.

Stay Hungry Stay Foolish
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Joined: 21 Aug 2013
Posts: 1428
Location: India
Re: From a class of 12 students, two students will be randomly chosen simu  [#permalink]

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31 Jan 2018, 09:45
Aekagra wrote:
What is OA? M confused.

Stay Hungry Stay Foolish

Hi

OA will be revealed on 6th Feb as the question says. Though if you go through the 2 solutions posted above you could see that they have explained the answer to be A.

Whats the confusion about may I know?
Intern
Joined: 04 Feb 2018
Posts: 1
Re: From a class of 12 students, two students will be randomly chosen simu  [#permalink]

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04 Feb 2018, 02:25
2) The probability that one boy and one girl will be chosen is 16/33..
Whatever Ans we get can be of boys or girls..
So insufficient..
(12-g)/12 *g/11* 2=16/33....... (12-g)g=32...

How do we get this 2 in the left side of equation?
Thank you!
Intern
Joined: 31 Oct 2017
Posts: 3
Re: From a class of 12 students, two students will be randomly chosen simu  [#permalink]

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04 Feb 2018, 06:35
chetan2u wrote:
Bunuel wrote:
From a class of 12 students, two students will be randomly chosen simultaneously. If g is the number of girls in the class, what is the value of g?

(1) The probability that two girls will be chosen together is 1/11.
(2) The probability that one boy and one girl will be chosen is 16/33.

Let the number of girl be g, then the number of boys =12-g...

(1) The probability that two girls will be chosen together is 1/11.
P of first as girl = g/12..
P of second as girl = (g-1)/11..
Combined prob = g/12 * (g-1)/11=1/11...
g (g-1)=12=4*3...
So g is 4
Sufficient..
2) The probability that one boy and one girl will be chosen is 16/33..
Whatever Ans we get can be of boys or girls..
So insufficient..
(12-g)/12 *g/11 * 2=16/33....... (12-g)g=32...
So g can be 8 or 4..
Insuff

A

Hi, thanks for the answer.
I still don't understand though where you got the 2 from in statement 2 :
(12-g)/12 *g/11 * 2=16/33....... (12-g)g=32...

DS Forum Moderator
Joined: 21 Aug 2013
Posts: 1428
Location: India
From a class of 12 students, two students will be randomly chosen simu  [#permalink]

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04 Feb 2018, 22:04
1
tahina wrote:
chetan2u wrote:
Bunuel wrote:
From a class of 12 students, two students will be randomly chosen simultaneously. If g is the number of girls in the class, what is the value of g?

(1) The probability that two girls will be chosen together is 1/11.
(2) The probability that one boy and one girl will be chosen is 16/33.

Let the number of girl be g, then the number of boys =12-g...

(1) The probability that two girls will be chosen together is 1/11.
P of first as girl = g/12..
P of second as girl = (g-1)/11..
Combined prob = g/12 * (g-1)/11=1/11...
g (g-1)=12=4*3...
So g is 4
Sufficient..
2) The probability that one boy and one girl will be chosen is 16/33..
Whatever Ans we get can be of boys or girls..
So insufficient..
(12-g)/12 *g/11 * 2=16/33....... (12-g)g=32...
So g can be 8 or 4..
Insuff

A

Hi, thanks for the answer.
I still don't understand though where you got the 2 from in statement 2 :
(12-g)/12 *g/11 * 2=16/33....... (12-g)g=32...

Hi

I think the '2' here is because there could be two cases: Either first student chosen is a boy, second one is a girl OR first student chosen is a girl, second one is a boy.

And for each of these two cases, Probability will be the same = [(12-g)*g] / [12*11].
So rather than add the two cases, he has multiplied by '2'.
From a class of 12 students, two students will be randomly chosen simu &nbs [#permalink] 04 Feb 2018, 22:04
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