Let X denotes no. of white balls 

$$\begin{gathered} \mathrm{P}(\mathrm{X}=0)=\frac{3}{7}\times \frac{3}{7}=\frac{9}{49} \\ \mathrm{P}(\mathrm{X}=1)=\frac{4}{7}\times \frac{3}{7}+\frac{3}{7}\times \frac{4}{7}=\frac{24}{49} \\ \mathrm{P}(X=2)=\frac{4}{7}\times \frac{4}{7}=\frac{16}{49} \end{gathered}$$

Mean $=\sum _{ }\mathrm{x} \mathrm{P}\left(\mathrm{x}\right)$

           $$\begin{gathered} =0+1\left(\frac{24}{49}\right)+2\left(\frac{16}{49}\right) \\ =\frac{56}{49} \\ =\frac{8}{7} \end{gathered}$$