A game at the fair involves a wheel with seven sectors. Two of the sectors are red, two of the sectors are purple, two of the sectors are yellow, and one sector is blue.

Landing on the blue sector will give 3 points, landing on a yellow sector will give 1 point, landing on a purple sector will give 0 points, and landing on a red sector will give –1 point.
Let X = the points you have after one spin. Fill out the missing values in the table.



If you take one spin, what is your expected value?



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.