What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. Thank you!

Answer with explanation:
⇒A game will be fair , if there is equal chance of winning and losing.
→The game would be fair , if
Landing on Blue sector gives 3.5 points.
Then the, Expected value will be
[tex]E(x_{i})=x_{i} \times P(x_{i})\\\\E(x)=x_{1} \times P(x_{1})+x_{2} \times P(x_{2})+x_{3} \times P(x_{3})+x_{4} \times P(x_{4})\\\\E(x)=-1 *\frac{2}{7}+(0) *\frac{2}{7}+(1) *\frac{2}{7}+(3.5) *\frac{1}{7}\\\\E(x)=(3.5) *\frac{1}{7}\\\\E(x)=0.50[/tex]
→→By Assigning, Blue sector =3.5 points, the game will become fair, Gives, E(x)=0.50.