A certain jar contains only b black marbles...

[sbosshard]

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

Can you help me figure out where to start when approaching this problem (answer according to GMAT prep CAT test is A.

Thanks,
Stephan

[cyber_office]

Hi,

My interpretation is as follows:

Since Statement 1 reads that r/(b+w) > w/(b+r), we can conclude that r/w must be > w/r since b is common to both denominators. It follows that r > w and hence r has a greater probability of being picked since there are more r marbles than w marbles.

Statement doesn't appear to provide much information: b - w > r. Alternatively, re-arranging, b - r > w. So it's a dead-end.

Not sure whether my logic is completely accurate, but the aforementioned approach is what I would have used on the test.

Regards.

[bortheratyourside]

now the probability of choosing r = r / ( b + w + r) ; the probability of choosing w is w / ( b + w+ r)...

Now S(1) tells us r/ (b+w) > w/ (b + r).. notice in the denominator, the numerator terms does not exist. it it did exist then we could solve the problem
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now S(1) can be re written as..
b+w/ r < b +r / w

add 1 to both sides
((b+w)/r )+ 1 < ((b +r)/ w)+ 1

b + w + r/r < b + w + r / w

invert the inequality
r/ ( b + w +r) > w / ( b + w+ r)

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ergo
s1 is good

[RonPurewal]

look here:

a-certain-jar-contains-only-b-black-marbles-t881.html

12 posts, so your question is probably answered in there somewhere.