Harish Dorai 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 is red greater than the probability that the marble chosen will be white?

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

2) b - w > r

The question asks whether r/(b+w+r) > w/(b+w+r) or in other words is r > w?

1. r(b+r) > w(b+w)

br + r^2 > bw + w^2

br - bw > w^2 - r^2

b(r-w) > (w-r)(w+r)

r-w > (w-r)(w+r)/b ----> We know b is positive. So, we can divide both sides without changing the inequality

r-w > k(w-r) ----> Where k > 0 as b,r and w are all positive

This is true only when r > w.

If r < w, left side is -ve and right side is +ve and the inequality doesn't hold.

SUFFICIENT.

2. b - w > r

b > w + r

This doesn't tell us anything about relationship between w and r.

INSUFFICIENT.

Answer is A.