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the difference in the probability

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by sanju09 » Thu Dec 26, 2013 1:48 am
Mycroft has a bag that only contains few red, blue, and green nuggets of identical shape, size, and weight. Two nuggets are randomly drawn from the bag, without replacement. What is the difference in the probability that both nuggets so drawn are red and the probability that none is green?

(1) Mycroft has ¾ as many red nuggets as the blue nuggets in his bag, which contains 1 green nugget more than the red nuggets.

(2) The probability that "either nuggets so drawn are red or none is green" is 53/105.


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Source: — Data Sufficiency |
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by theCodeToGMAT » Fri Dec 27, 2013 9:28 am
R, B, G --> 2 are drawn

To find: Prob of Red -(Prob of NOT Green) ==> [(R)(R-1) - (R+B)(R+B-1)]/(R+B+G)(R+B+G-1)

Statement 1:
3/4 R = B ==> 3R = 4B
G = R + 1
If B = 3, then R = 4 & G = 5 ==> Probability = |(4x3 - 7x6)|/(12)(11) = 30/12*11 = 5/22
If B = 6, then R = 8 & G = 9 ==> probability = | 8x7 - 14x13|/(23)(22) = 126/23*22 = 63/263
INSUFFICIENT

Statement 2:
((R)(R-1) + (R+B)(R+B-1))/(R+B+G)(R+B+G-1) = 53/120
we cannot conclude on separate probabilities
INSUFFICIENT

Combining...
((R)(R-1) + (R+B)(R+B-1))/(R+B+G)(R+B+G-1) = 53/120
we can convert the equation say in terms of "R" using:
3/4 R = B
G = R + 1
IF we get R then we can get all other values
SUFFICIENT

Answer [spoiler]{C}[/spoiler]?
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by sanju09 » Sat Dec 28, 2013 12:00 am
theCodeToGMAT wrote:R, B, G --> 2 are drawn

To find: Prob of Red -(Prob of NOT Green) ==> [(R)(R-1) - (R+B)(R+B-1)]/(R+B+G)(R+B+G-1)

Statement 1:
3/4 R = B ==> 3R = 4B
G = R + 1
If B = 3, then R = 4 & G = 5 ==> Probability = |(4x3 - 7x6)|/(12)(11) = 30/12*11 = 5/22
If B = 6, then R = 8 & G = 9 ==> probability = | 8x7 - 14x13|/(23)(22) = 126/23*22 = 63/263
INSUFFICIENT

Statement 2:
((R)(R-1) + (R+B)(R+B-1))/(R+B+G)(R+B+G-1) = 53/120
we cannot conclude on separate probabilities
INSUFFICIENT

Combining...
((R)(R-1) + (R+B)(R+B-1))/(R+B+G)(R+B+G-1) = 53/120
we can convert the equation say in terms of "R" using:
3/4 R = B
G = R + 1
IF we get R then we can get all other values
SUFFICIENT

Answer [spoiler]{C}[/spoiler]?
Nice thought process Rahul. But you must thank it was DS, had it been PS, you'd have paid heavily for reading 105 as 120.

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by theCodeToGMAT » Sat Dec 28, 2013 8:26 am
sanju09 wrote:
Nice thought process Rahul. But you must thank it was DS, had it been PS, you'd have paid heavily for reading 105 as 120.

Best
ooops......
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