A player tosses two coins. He wins Rs.1 if 1 head appears, Rs 2 if 2 heads appear. But he lose Rs 5 if no head appears. The mean of the prized money is 
 

X denotes the amount he wins then. X takes values -5, 1, 2

Now $\mathrm{P}(\mathrm{x}=0)=\frac{{}^2\mathrm{C}_0}{2^2}=\frac{1}{4}$

         $\mathrm{P}(\mathrm{x}=1)=\frac{{}^2\mathrm{C}_1}{2^2}=\frac{1}{2}$

         $\mathrm{P}(\mathrm{x}=2)=\frac{{}^2\mathrm{C}_2}{2^2}=\frac{1}{4}$

Then probability distribution of X is

mean $\left(\overline{\mathrm{x}}\right)=\sum {\mathrm{x}}_{\mathrm{i}} \mathrm{P}(\mathrm{X}={\mathrm{x}}_{\mathrm{i}})$

                 $$\begin{gathered} =(-5)\left(\frac{1}{4}\right)+1\left(\frac{1}{2}\right)+2\left(\frac{1}{4}\right) \\ =-\frac{1}{4} \end{gathered}$$