A simple game goes as follows: you pay one dollar and roll a die. If the roll is either a 1 or 2, you get your dollar back. If it is greater than 3 you lose the dollar you paid. If it is a 3, you get your dollar back and an additional dollar. What is the expected value of the net amount of money you win/lose?

Answer:-1/3Step-by-step explanation:Given that a simple game goes as follows: you pay one dollar and roll a die. If the roll is either a 1 or 2, you get your dollar back. If it is greater than 3 you lose the dollar you paid. If it is a 3, you get your dollar back and an additional dollar. Your fee for the dollar would be 1 dollar alwaysIf you roll 1 or 2, your gain is 0If you roll 3, your gain is 1If you roll 4 or 5 or 6you lose 1 dollarLet X be the amount of gain.X       0        1         -1P       2/6     1/6      3/6   E(x) = Sum of products of x with probabilities= [tex]\frac{1}{6} -\frac{3}{6} \\=\frac{-2}{6} \\=\frac{-1}{3}[/tex]Note:  this is not a fair game to play since expected gain is negative.