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# a certain jar contains only b black marbles, w white

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a certain jar contains only b black marbles, w white [#permalink]

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03 Jun 2006, 22:21
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

a certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?
(1)r/(b+w) > w/(b+r)
(2) b-w>r
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Re: GMATPREP : marble probability [#permalink]

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04 Jun 2006, 11:12
shobhitb wrote:
dinesh8 wrote:
a certain jar contains only b black marbles, w white marbles, and r red marbles. If one marble is to be chosen at random from the jar, is the probability that the marble chosen will be red greater than the probability that the marble chosen will be white?
(1)r/(b+w) > w/(b+r)
(2) b-w>r

A

Can you explain how you got A?
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04 Jun 2006, 12:29
my guess A

2...does not help since it implies b > r+w

to say that the probability of choosing a red marble is higher than that of choosing a white marble we need to prove rC1/(r+w+b)C1 > wC1/(r+w+b)C1...i.e r>w

1 is r/(b+w) > w/(b+r)

i.e r(b+r) > w(b+w)

i.e br + r^2 > bw + w^2

i.e (r-w)(r+w) + b(r-w) > 0

since r,b,w are positive #'s this is possible only when r > w

so A
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05 Jun 2006, 00:41
I think its A.
Option 1) - It doesn't give complete info.
Option 2) -
Required probability for red is r/(r+w+b)
Required probability for white is w/(r+w+b)

From Eqn 1) we know that r/(b+w) > w/(b+r)
So by componendo & dividendo (C & D)
r/(b+w+r) > w/(b+r+w)
which is sufficient to answer this.

Please update if my approach is not correct.
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If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut.
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05 Jun 2006, 00:41
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