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# In a dice game, a player pays a stake of Re1 for each throw of a die.She receives Rs 5 if the die shows a 3,Rs 2 if the die shows a 1 or 6,and nothing otherwise.What is the player's expected profit per throw over a long series of throws?

• The possible outcum of throwof dice are${1\;,2\;,3\;,4\;,5\;,6\;}$ each having the probability$\Large\frac{1}{6}$
• Expected profit=$\Large\sum_{i=1}^{6} x_ip_i$
$E(x)=\Large1\times\;\frac{1}{6}\;+-1\times\;\frac{1}{6}\;+4\times\;\frac{1}{6}\;+-1\times\;\frac{1}{6}\;+-1\times\;\frac{1}{6}\;+1\times\;\frac{1}{6}$
=$\Large\frac{3}{6}$
=$0.05$