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

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Bunuel
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From a class of 12 students, two students will be randomly chosen simu [#permalink] New post   30 Jan 2018, 08:20
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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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chetan2u
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From a class of 12 students, two students will be randomly chosen simu [#permalink] New post   30 Jan 2018, 09:38
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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

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Re: From a class of 12 students, two students will be randomly chosen simu [#permalink] New post   30 Jan 2018, 21:57
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] New post   31 Jan 2018, 10:36
What is OA? M confused.

Stay Hungry Stay Foolish
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Re: From a class of 12 students, two students will be randomly chosen simu [#permalink] New post   31 Jan 2018, 10:45
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?
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Re: From a class of 12 students, two students will be randomly chosen simu [#permalink] New post   04 Feb 2018, 03:25
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!
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Re: From a class of 12 students, two students will be randomly chosen simu [#permalink] New post   04 Feb 2018, 07:35
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...

Many thanks in advance for your answer
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From a class of 12 students, two students will be randomly chosen simu [#permalink] New post   04 Feb 2018, 23:04
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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...

Many thanks in advance for your answer


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'.
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Re: From a class of 12 students, two students will be randomly chosen simu [#permalink] New post   29 Jul 2019, 17:11
I think this way for multiplication of 2 for st.2.

Ways of selecting of a boy. 12-gC1= 12-g
Ways of selecting of a girl gC1 = g
Ways of selecting 2 from 12 students = 12C2

Then he probability of selecting one boy and one girl is = (12-g)*g/(12*11/2)= 16/33

Now we will get multiplication of 2 as shown in your explanation.

YDW I still have a doubt. Why we could not solve it as below.
(12-g)/12 * g/11= 16/33
I have solved many such questions and got the correct answer. Probably, the given answer choice was wrong.
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Re: From a class of 12 students, two students will be randomly chosen simu [#permalink] New post   26 Dec 2022, 07:46
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Re: From a class of 12 students, two students will be randomly chosen simu [#permalink]
26 Dec 2022, 07:46
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