call I(1)=0 if the first ball we took out is black

I(1)=1 if the first ball we took out is white

same for I(2),

I(2)=1 if the second ball we took out is white

I(2)=0 if the second ball taken out is black

now X=I(1)

Y=I(1)+I(2)

compute E(Var(Y|X))

E stands for expectancy

Var stands for Variance

thanks for your help!