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

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Manager
Joined: 17 Jan 2006
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a certain jar contains only b black marbles, w white [#permalink]  03 Jun 2006, 22:21
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
Manager
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Re: GMATPREP : marble probability [#permalink]  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?
Senior Manager
Joined: 12 Mar 2006
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Schools: Kellogg School of Management
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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
Intern
Joined: 04 May 2006
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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.
_________________

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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