Question

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 1

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

`E(x_(i))=x_(i) * P(x_(i))\\\\E(x)=x_(1) * P(x_(1))+x_(2) * P(x_(2))+x_(3) * P(x_(3))+x_(4) * P(x_(4))\\\\E(x)=-1 *(2)/(7)+(0) *(2)/(7)+(1) *(2)/(7)+(3.5) *(1)/(7)\\\\E(x)=(3.5) *(1)/(7)\\\\E(x)=0.50`

→→By Assigning, Blue sector =3.5 points, the game will become fair, Gives, E(x)=0.50.