Re: A certain box contains only blue (b), green (g) and red(r)

A certain box contains only blue (b), green (g) and red(r) marbles. If one marble is to be picked out from the box at random, which color marble is most likely to be picked?

(1) b/(g+r) > r/(g+b)
Case b=10 g=1 r=1
\frac{10}{1+1}>\frac{1}{10+1} in this case the answer is blue
Case b=10 g=20 r=1
\frac{10}{20+1}>\frac{1}{10+20} in this case the answer is green
Not sufficient

(2) g > b
No info about r.
Not sufficient

(1+2)
b(g+b)>r(g+r)
bg+b^2>rg+r^2
b^2-r^2>rg-bg
(b+r)(b-r)>g(r-b)
CASE if r>b we have r-b>0 and b-r<0
(+)(-)>(+)(+)
(-)>(+) Not possible
CASE if b>r we have b-r>0 and r-b<0
(+)(+)>(+)(-) Possible
So we find out that b>r so g>b>r
The answer is G
C