The mean of the ‘Sixes’ in two tosses of an unbiased die is 
 

Let X denote the getting sixes on two dies

 when two dies are rolled X takes the values 0, 1, 2

Now $\mathrm{P}(X=0)={}^2\mathrm{C}_0{\left(\frac{5}{6}\right)}^{ }{\left(\frac{5}{6}\right)}^{ }=\frac{25}{36}$

         $$\begin{gathered} \mathrm{P}(X=1)={}^2\mathrm{C}_1{\left(\frac{1}{6}\right)}^{ }{\left(\frac{5}{6}\right)}^{ }=\frac{10}{36} \\ \mathrm{P}(X=2)={}^2\mathrm{C}_2{\left(\frac{1}{6}\right)}^{ }\left(\frac{1}{6}\right)=\frac{1}{36} \end{gathered}$$

then probability distribution of X is

Mean $=\sum {\mathrm{x}}_{\mathrm{i}} \mathrm{P}(X={\mathrm{x}}_{\mathrm{i}})$

           $$\begin{gathered} =0\left(\frac{25}{36}\right)+1\left(\frac{10}{36}\right)+2\left(\frac{1}{36}\right) \\ =\frac{12}{36} \\ =\frac{1}{3} \end{gathered}$$