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# m25, #27

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01 Dec 2008, 06:27
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The bowl contains chips of red and green color and no chips of any other color. If two chips are drawn from the basket at random without replacement, what is the probability that both chips will be green?

1. 20% of all chips in the basket are green
2. The ratio of the number of red chips to the number of green chips is 4:1

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Shldnt the answer be D. bcos from both (1) and (2), we know the probabiliy of taking out a green chip=1/5 and hence the probability can be claculated.

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01 Dec 2008, 07:11
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ritula wrote:
The bowl contains chips of red and green color and no chips of any other color. If two chips are drawn from the basket at random without replacement, what is the probability that both chips will be green?

(1)20% of all chips in the basket are green
(2)The ratio of the number of red chips to the number of green chips is 4:1

Shldnt the answer be D. bcos from both (1) and (2), we know the probabiliy of taking out a green chip=1/5 and hence the probability can be claculated.

I did go in for D. But, realised (1) & (2) are the same, if you equate it.

I think the answer is E

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01 Dec 2008, 07:18
Just percentage will not be sufficient to get the probability. Look at two examples below with with same 20% green chips

Red chips = 8
Green chips = 2
Hence, probability of getting 2 green chips = 2C2/10C2 = 2/45

Or, red chips = 16
Green chips = 4
And probability = 4C2 / 20C2 = 3/95

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01 Dec 2008, 15:57
i think percentage is sufficient??

scthakur wrote:
Just percentage will not be sufficient to get the probability. Look at two examples below with with same 20% green chips

Red chips = 8
Green chips = 2
Hence, probability of getting 2 green chips = 2C2/10C2 = 2/45

Or, red chips = 16
Green chips = 4
And probability = 4C2 / 20C2 = 3/95

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02 Dec 2008, 00:07
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The bowl contains chips of red and green color and no chips of any other color. If two chips are drawn from the basket at random without replacement, what is the probability that both chips will be green?

(1)20% of all chips in the basket are green
(2)The ratio of the number of red chips to the number of green chips is 4:1

Shldnt the answer be D. bcos from both (1) and (2), we know the probabiliy of taking out a green chip=1/5 and hence the probability can be claculated.

Percentage is not suffiecient. What if there is 1 green chip and 4 red chips? You have a 1/5 chance of hitting green on the first try, and a 0% chance of hitting green on the second try. 1 & 4 fulfill the requirements for both (1) and (2). Picking different numbers for greens and reds will obviously yield a different result than 0%.

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23 Jan 2010, 01:36
yeah, i made the same mistake of opting for D. didn't realize it was a tricky question where both the statements provided the same information. should have tried plugging in numbers. that would prove it's E

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01 Jul 2010, 05:05
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IMO E

Both statements provides same ratio or persent. If we plug in value according to ratios or percent given, probability will change every time. Total number of chips are required to answer.

Another tip - When both statements gives same info (they are deadly twins) then answer is surely E
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01 Jul 2010, 06:25
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Will go with E , as even with both the statements we will not be able to identify the exact number. Question takes in terms of ration(%) and requires more information to calculate exact numbers
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01 Jul 2010, 21:52
I think the answer is either one. The answer here should be 1/5 as whether you take 2 or 3 or more upto 20 balls it should be same set of choices with you. Above 20 the prob will become 0.

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01 Jul 2010, 23:52
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green to red:
(i)4 : 1 P(G) x P(G) = 1/4 x 0 = 0
(ii)8 : 2 P(G) x P(G) = 1/10 x 1/9 = 1/90
(iii)12 : 3 P(G) x P(G) = 3/15 x 2/14 = 1/35

in all instances the probabilities are the same for the first pick;
however, the second picks produced different results depending
on the initial number of balls.
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05 Jul 2011, 05:07
If there are R red and G green, then probably of 2 greens
= P(1st Green) * P(2nd Green)
= [G/(G+R)] * [(G-1)/(G+R-1)]

1st part can be factored if ratio R:G is given, BUT NOT the 2nd part.

Good question though. My instinct was D as soon as I read the problem but when I processed the equation in mind I realized it's not trivial and is a trap question

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05 Jul 2011, 06:13
The answer is E. And here's why.

First of all both the statements say the same thing, i.e. green balls are 20% and red balls are 80% of the total balls in the bag. So if we evaluate whether one's sufficient, we can safely assume the same about the other statement too.

now, we know that balls are in the ratio of G:R = 1:4, hence the actual probability that the first ball will be green is 1x/5x. However, the probability that the second ball will be green is 1x-1/5x-1. By multiplying these two, we can not come to a conclusive answer. Hence E

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05 Jul 2011, 06:13
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ritula wrote:
The bowl contains chips of red and green color and no chips of any other color. If two chips are drawn from the basket at random without replacement, what is the probability that both chips will be green?

1. 20% of all chips in the basket are green
2. The ratio of the number of red chips to the number of green chips is 4:1

Stmt1: Let there be 100 chips.
Green chips = 20
Probability of picking two green chips = 20/100 * 19/99 = 0.2 * 19/99
Let there be 200 chips
Green chips= 40
Probability of picking two green chips = 40/200 * 39/199 = 0.2 * 39/199
Hence two different values depending on total number of chips. Not sufficient

Stmt2: The ratio of the number of red chips to the number of green chips is 4:1
Red=8
Green=2
Total = 10
Probability of picking two green chips = 2/10 * 1/9 = 0.2 * 1/9

Red=16
Green=4
Total =20
Probability of picking two green chips=4/20 * 3/19 = 0.2 * 3/19.
Again different probability for different number of of total chips. Insufficient.

Together, also, total number of chip is still missing which is key data needed to answer the question.
OA E.

P.S: Note if question had asked probability of picking 1 green chip, answer would have been D. as in each statement we would have been able to tell probability (0.2) in cases above.
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05 Jul 2011, 18:30
It's E. Probability can change when actual nos are put in place of ratios for successive draws.

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06 Jul 2011, 03:02
Ans is [E]. Such DS problems in which each statement provides the same info by twisting them a little bit (in this case ratios and percents) are quite common. I reckon such type of problems come in the 600-700 category

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14 Mar 2012, 11:03
scthakur wrote:
Just percentage will not be sufficient to get the probability. Look at two examples below with with same 20% green chips

Red chips = 8
Green chips = 2
Hence, probability of getting 2 green chips = 2C2/10C2 = 2/45

Or, red chips = 16
Green chips = 4
And probability = 4C2 / 20C2 = 3/95

Yes, bingo!

But, it would've been a different case if just one chip was drawn

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27 Mar 2012, 01:45
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ritula wrote:
The bowl contains chips of red and green color and no chips of any other color. If two chips are drawn from the basket at random without replacement, what is the probability that both chips will be green?

1. 20% of all chips in the basket are green
2. The ratio of the number of red chips to the number of green chips is 4:1

[Reveal] Spoiler: OA
E

Source: GMAT Club Tests - hardest GMAT questions

Shldnt the answer be D. bcos from both (1) and (2), we know the probabiliy of taking out a green chip=1/5 and hence the probability can be claculated.

A bowl contains red and green chips and no chips of any other color. If two chips are drawn from the basket at random without replacement, what is the probability that both chips will be green?

(1) 20% of all chips in the basket are green --> 80% of all chips in the basket are red --> the ratio of the number of red chips to the number of green chips is 4:1 (80:20). Now, if there are total of 5 chips in the bowl (4 red + 1 green) then the the probability that both chips will be green will be 0 (since there are NOT two chips in a bowl) but if there are total of 10 chips in the bowl (8 red + 2 green) then the the probability that both chips will be green will be more than 0. Not sufficient.

(2) The ratio of the number of red chips to the number of green chips is 4:1. The same info as above. Not sufficient.

(1)+(2) Both statements tell the same thing, so we have no new info. Not sufficient.

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27 Mar 2012, 03:34
Ya even I fell for the deadly twins
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09 Jul 2012, 05:29
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Never attempt to solve successive draws probability if you only have ratios and not the actual number. That said answer is E, since both statements say the same thing.

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09 Jul 2013, 13:48
So
1) Using 10 as the number 20% of 10 is 2 so 2/10. Insufficient for A
2) 1:4 no matter what number used is insufficient for B.
1 and 2 conflict 20% vs 25% C is insufficient
1 and 2 both don't stand alone so D is insufficient.
That leaves E.

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# m25, #27

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