Jar of black, white and red marbles - probability

[wally]

A certain jar contains only [i]b[/i] black marbles , [i]w[/i] white marbles, and [i]r[/i] 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

ANSWER: [spoiler]A[/spoiler]

[sacx]

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

we can cross multiply since b,r,w can only be positive

rb + wr + r^2 > wb + w^2 + wr
rb + r^2 > wb + w^2

Stmt I

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

rb + r^2 > wb + w^2

Suff

Stmt II

b-w > r
b > w+r

does not give any relationship between white and red balls

Insuff

Choose A

[Ian Stewart]

I suggested two non-algebraic ways to look at the problem here:

www.beatthegmat.com/marbles-probability-t32705.html

There's also an algebraic solution in that thread.