Math problem : Reloaded!

[whyBish]

let w=white balls in jar1
let b=blanck balls in jar1
0<=b<=50
0<=w<=50

chance of winning: (for b<>0 and w<>50)

2P=chance of white in jar1 + chance of white in jar2
=w/(b+w)+(50-w)/(100-b-w)

2dP/dw=[(b+w)-w]/b^2+[-1(100-b-w)--1(50-w)]/(100-b-w)^2
=1/b+[-100+b+w+50-w]/(100-b-w)^2
=1/b+(b-50)/(100-b-w)^2

2d^2P/dw^2=[-(b-50)(-2(100-b-w))/(100-b-w)^4
=2(b-50)/(100-b-w)^3
so Pww <0

2dP/db=-w/(b+w)^2+(50-w)/(100-b-w)^2

2d^2P/db^2=2w/(b+w)^3-(50-w)(-2(100-b-w))/(100-b-w)^4
=2w/(b+w)^3+2(50-w)/(100-b-w)^3
so Pbb >0