Step 1:

Let $X$ be the random variable denoting the amount that a man can win when 3 coins are tossed once.

$X$ takes the values Rs.10,-Rs.5

Step 2:

$P(X=10)$=Probability of all heads or all tails

$\qquad\quad\;\;\;=2\times (\large\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2})$

$\qquad\quad\;\;\;=\large\frac{1}{4}$

$P(X=-5)=1-\large\frac{1}{4}=\frac{3}{4}$

Step 3:

The probability distribution of $x$ is given by

Step 4:

$E(X)$=expectation of gain =$\sum x_iP_i$

$\qquad=10\times \large\frac{1}{4}$$+(-5)\times \large\frac{3}{4}$

$\qquad=\large\frac{10-15}{4}$

$\qquad=\large\frac{-5}{4}$

$\qquad=-1.25$

He is expected to lose Rs.1.25