Question

A fair die is tossed. If $2,3$ or $5$ occurs, the player wins that number of rupees, but if $1,4$ or $6$ occurs, the player loses that number of rupees. Then find the possible payoffs for the player.

Answer 1

$A_i$	$2$	$3$	$5$	$1$	$4$	$6$
$M_i$	$2$	$3$	$6$	$-1$	$-4$	$-6$
$P_i$	$1/6$	$1/6$	$1/6$	$1/6$	$1/6$	$1/6$

Then expected value $E$ of the game payoffs for the player
$=2\left(\frac{1}{6}\right)+3\left(\frac{1}{6}\right)+5\left(\frac{1}{6}\right)-1\left(\frac{1}{6}\right)-4\left(\frac{1}{6}\right)-6\left(\frac{1}{6}\right)=-\left(\frac{1}{6}\right)$
Since $E$ is negative therefore game is unfavorable to the player.