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# gmat prep-6

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Senior Manager
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22 Aug 2009, 09:56
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I've got troubles to answer some of the gmat prep questions. The solutions will be appreciated with kudos . Thanks for the help
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Please give kudos if you enjoy the explanations that I have given. Thanks

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Re: gmat prep-6 [#permalink]

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22 Aug 2009, 10:08
so you know there are 45 rocks total and you want to pick 2 rocks out without replacement resulting in slate rocks. So you have something like:
1st pick: 15/45 (a chance to pick 1 of 15 slate rocks out of 45 total)
2nd pick: 14/44 (a chance to pick another slate rock of the 14 left out of 44)
15/45 * 14/44 = 1/3*7/22 = 7/66
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Re: gmat prep-6 [#permalink]

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22 Aug 2009, 10:38
Please note my answers are wrong. So D is wrong in this case.
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Manager
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Re: gmat prep-6 [#permalink]

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24 Aug 2009, 21:02
shaselai wrote:
so you know there are 45 rocks total and you want to pick 2 rocks out without replacement resulting in slate rocks. So you have something like:
1st pick: 15/45 (a chance to pick 1 of 15 slate rocks out of 45 total)
2nd pick: 14/44 (a chance to pick another slate rock of the 14 left out of 44)
15/45 * 14/44 = 1/3*7/22 = 7/66

it should be 1/9. the statement says rocks are selected without replacement
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Re: gmat prep-6 [#permalink]

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24 Aug 2009, 21:18
perfectstranger wrote:
Please note my answers are wrong. So D is wrong in this case.

I am subscribing to the post only to know the explaination from an expert. According to me, the answer is 7/66. But it could also be 1/9 by POE. Lets see.
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Re: gmat prep-6 [#permalink]

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25 Aug 2009, 05:14
Ibodullo wrote:
shaselai wrote:
so you know there are 45 rocks total and you want to pick 2 rocks out without replacement resulting in slate rocks. So you have something like:
1st pick: 15/45 (a chance to pick 1 of 15 slate rocks out of 45 total)
2nd pick: 14/44 (a chance to pick another slate rock of the 14 left out of 44)
15/45 * 14/44 = 1/3*7/22 = 7/66

it should be 1/9. the statement says rocks are selected without replacement

but isnt my answer without replacement? for my 2nd pick the total rock is 1 less and there are only 14 slate rocks to pick from?
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Re: gmat prep-6 [#permalink]

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25 Aug 2009, 05:33
are you sure that the answer is not D?
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Re: gmat prep-6 [#permalink]

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25 Aug 2009, 13:01
Without replacement: D
With replacement: C

Do I have an incorrect definition of replacement?
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Re: gmat prep-6 [#permalink]

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25 Aug 2009, 13:22
Guys answer is A:

lets work out:

i cant explain the full thing but pls bear wid me...

prob = 1 - (prob selcting 1st no*prob not selcting 2nd no from the list) - ( prob selcting 2nd no*prob not selcting 1st no from the list) - (prob NOT selcting 1st no*prob NOT selcting 2nd no from the list)

NOTE: its 1 - ( p1 + p2 + p3 ) = 1- p1 -p2 -p3

now 15/45 = 1/3

prob = 1 - 1/3 * 14/44 - 1/3 * 14/44 - 30/45 *30/ 44

prob = 1/3

Pls if i am correct , dont hasitate in giving me my share lol........

if not then lets wait for the right solution.....cheers
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Re: gmat prep-6 [#permalink]

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25 Aug 2009, 16:30
rohansherry wrote:
Guys answer is A:

lets work out:

i cant explain the full thing but pls bear wid me...

prob = 1 - (prob selcting 1st no*prob not selcting 2nd no from the list) - ( prob selcting 2nd no*prob not selcting 1st no from the list) - (prob NOT selcting 1st no*prob NOT selcting 2nd no from the list)

NOTE: its 1 - ( p1 + p2 + p3 ) = 1- p1 -p2 -p3

now 15/45 = 1/3

prob = 1 - 1/3 * 14/44 - 1/3 * 14/44 - 30/45 *30/ 44

prob = 1/3

Pls if i am correct , dont hasitate in giving me my share lol........

if not then lets wait for the right solution.....cheers

Hi,
why not 30/45*29/44 ?

This answer seems better indeed, I think it's the right answer.
Thanks
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Re: gmat prep-6 [#permalink]

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25 Aug 2009, 16:39
mendelay wrote:
Without replacement: D
With replacement: C

Do I have an incorrect definition of replacement?

No, you have a correct definition of replacement. "Without replacement" means that events are dependent and we are dealing with conditional probability.
Define events:
A - first drawn rock is slate
B - second drawn rock is slate

$$P(A)=\frac{15}{45}=\frac{1}{3}$$ (since we have 15 slate rocks and 45 total)
$$P(B/ A)=\frac{14}{44}=\frac{7}{22}$$ (since after first slate is drawn, we have 14 slate rocks and 44 total)
$$P(A and B)=P(A)\timesP(B/ A)=\frac{1}{3}\times\frac{7}{22}=\frac{7}{66}$$

There is a mistake in the question for sure. It is either "with replacement" and the answer $$\frac{1}{9}$$ or "without replacement" and the answer $$\frac{7}{66}...$$
Manager
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Re: gmat prep-6 [#permalink]

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25 Aug 2009, 19:51
LenaA wrote:
mendelay wrote:
Without replacement: D
With replacement: C

Do I have an incorrect definition of replacement?

No, you have a correct definition of replacement. "Without replacement" means that events are dependent and we are dealing with conditional probability.
Define events:
A - first drawn rock is slate
B - second drawn rock is slate

$$P(A)=\frac{15}{45}=\frac{1}{3}$$ (since we have 15 slate rocks and 45 total)
$$P(B/ A)=\frac{14}{44}=\frac{7}{22}$$ (since after first slate is drawn, we have 14 slate rocks and 44 total)
$$P(A and B)=P(A)\timesP(B/ A)=\frac{1}{3}\times\frac{7}{22}=\frac{7}{66}$$

There is a mistake in the question for sure. It is either "with replacement" and the answer $$\frac{1}{9}$$ or "without replacement" and the answer $$\frac{7}{66}...$$

The question does mention that the rock a picked without replacement. Thanks LenaA, good explanation.
Senior Manager
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Re: gmat prep-6 [#permalink]

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26 Aug 2009, 01:02
vuhuong wrote:
rohansherry wrote:
Guys answer is A:

lets work out:

i cant explain the full thing but pls bear wid me...

prob = 1 - (prob selcting 1st no*prob not selcting 2nd no from the list) - ( prob selcting 2nd no*prob not selcting 1st no from the list) - (prob NOT selcting 1st no*prob NOT selcting 2nd no from the list)

NOTE: its 1 - ( p1 + p2 + p3 ) = 1- p1 -p2 -p3

now 15/45 = 1/3

prob = 1 - 1/3 * 14/44 - 1/3 * 14/44 - 30/45 *30/ 44

prob = 1/3

Pls if i am correct , dont hasitate in giving me my share lol........

if not then lets wait for the right solution.....cheers

Hi,
why not 30/45*29/44 ?

This answer seems better indeed, I think it's the right answer.
Thanks

Prob of not selecting teh second would be = 1 -14/44 = 30/44

PLs post the OA . i am so very curious to know if i am right
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Re: gmat prep-6 [#permalink]

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26 Aug 2009, 08:16
rohansherry wrote:
Guys answer is A:

lets work out:

i cant explain the full thing but pls bear wid me...

prob = 1 - (prob selcting 1st no*prob not selcting 2nd no from the list) - ( prob selcting 2nd no*prob not selcting 1st no from the list) - (prob NOT selcting 1st no*prob NOT selcting 2nd no from the list)

NOTE: its 1 - ( p1 + p2 + p3 ) = 1- p1 -p2 -p3

now 15/45 = 1/3

prob = 1 - 1/3 * 14/44 - 1/3 * 14/44 - 30/45 *30/ 44

prob = 1/3

Pls if i am correct , dont hasitate in giving me my share lol........

if not then lets wait for the right solution.....cheers

Your approach is correct but calculation of probabilities is wrong. going your way, the result is still 7/66.
Define 4 possible outcomes of selecting 2 rocks.
P(S, NS) - probability to select 1st slate and 2nd nonslate
P(S,S) - 1st slate and 2nd slate
P(NS,S) - 1st non slate and 2nd slate
P(NS,NS) - 1st non slate and 2nd non slate

P(S,NS)+P(S,S)+P(NS,S)+P(NS,NS)=1
To find P(S,S), you have 2 approaches
1) Direct one as I showed before. $$\frac{1}{3}\times\frac{14}{44}$$
2) Not direct:
1-(P(S,NS)+P(NS,S)+P(NS,NS))=P(S,S)

P(S, NS) - $$\frac{1}{3}\times\frac{30}{44}$$
P(NS,S) - $$\frac{2}{3}\times\frac{15}{44}$$
P(NS,NS) -$$\frac{2}{3}\times\frac{29}{44}$$

p(S,S) = $$1-(\frac{1}{3}\times\frac{30}{44}+\frac{2}{3}\times\frac{15}{44}+\frac{2}{3}\times\frac{29}{44})=1-\frac{118}{132}=\frac{7}{66}$$

It is can be visualized by drawing a binary tree. It is always helpful not to get confused with conditional probs.

Sorry for edits...trying to figure out how to write formulas
Re: gmat prep-6   [#permalink] 26 Aug 2009, 08:16
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