In a game, a person is paid Rs. 2 if he gets all heads or all tails when three coins are tossed, and he will pay Rs. 2 if either one or two heads show. What can he expect to win on an average per game?

Lose Rs. 1 per toss of the coins.

The correct answer is Option (1) → Lose Rs. 1 per toss of the coins.

$\text{Total outcomes when 3 coins are tossed}=8$

$\text{All heads or all tails: } \{HHH,TTT\}\Rightarrow 2 \text{ outcomes}$

$\text{Exactly 1 or 2 heads: } 6 \text{ outcomes}$

$\text{Payoff:}$

$+2 \text{ for } 2 \text{ outcomes},\quad -2 \text{ for } 6 \text{ outcomes}$

$\text{Expected value }E=\frac{2(+2)+6(-2)}{8}$

$= \frac{4-12}{8}$

$= \frac{-8}{8}$

$= -1$

The person can expect to lose Rs. 1 per game.