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# A bag consists of 2 red balls, 3 blue balls and 4 green balls

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GMAT Forum Moderator
Joined: 28 May 2014
Posts: 475
GMAT 1: 730 Q49 V41
A bag consists of 2 red balls, 3 blue balls and 4 green balls [#permalink]

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10 Jan 2018, 13:34
1
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Difficulty:

35% (medium)

Question Stats:

67% (02:03) correct 33% (00:57) wrong based on 24 sessions

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A bag consists of 2 red balls, 3 blue balls and 4 green balls. If Andy picks up two balls from the bag one by one without replacement, what is the probability that the balls picked up are of different colors?

A) 5/9
B) 49/72
C) 17/24
D) 13/18
E) 15/17
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Aug 2009
Posts: 5713
A bag consists of 2 red balls, 3 blue balls and 4 green balls [#permalink]

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10 Jan 2018, 17:43
saswata4s wrote:
A bag consists of 2 red balls, 3 blue balls and 4 green balls. If Andy picks up two balls from the bag one by one without replacement, what is the probability that the balls picked up are of different colors?

A) 5/9
B) 49/72
C) 17/24
D) 13/18
E) 15/17

There can be two ways..
1) finding the prob of same colour and then subtracting from 1..
Prob of same colour$$\frac{2*1}{9*8}+\frac{3*2}{9*8}+\frac{4*3}{9*8}=\frac{2*1+3*2+4*3}{9*8}=\frac{20}{72}=\frac{5}{18}$$..
So ans is $$1-\frac{5}{18}=\frac{13}{18}$$
D
2) finding prob of different colours..
Red and blue =2* 2/9*3/8=1/6
Red and green = 2* 2/9*4/8=2/9
Blue and green = 2*3/9*4/8=1/3
So total = 1/6+1/3+2/9=13/18
D
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Posts: 65
Re: A bag consists of 2 red balls, 3 blue balls and 4 green balls [#permalink]

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10 Jan 2018, 18:40
1
KUDOS
Selecting:
case 1: red & others = (2/9)*(7/8)
case 2: blue & others = (3/9)*(6/8)
case 3: green & others = (4/9)*(5/8)
Sum of all 3 cases = 13/18
Re: A bag consists of 2 red balls, 3 blue balls and 4 green balls   [#permalink] 10 Jan 2018, 18:40
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