Question

A player tosses two coins. He wins $Rs.1$ if one head appears, $Rs.2$ if two heads appear. But he loss $Rs.5$. if two tail appears. The sum of the prize money is,

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
  
• C. $\frac{-1}{4}$
• D. $\frac{1}{5}$

Answer 1

The correct option is C $\frac{-1}{4}$

$WhenplayerlossRs.5⟹$ {TT} $⟹$$x=-5$ $⟹$ $P\left(x\right)=\frac{1}{4}$

$WhenplayerwinsRs.1⟹${HT,TH} $⟹$$x=1$, $⟹$ $P\left(x\right)=\frac{1}{2}$

$WhenplayerwinsRs.2⟹${HH}$⟹$$x=2$, $⟹$$P\left(x\right)=\frac{1}{4}$

$E\left(x\right)=sumofxP(X=x)$ $=(1\times \frac{1}{2})+(2\times \frac{1}{4})-(5\times \frac{1}{4})=\frac{-1}{4}$

Hence option $C$ is the answer.