1. A game at thefair involves a wheel with seven sectors. Two of the sectors are pink, two of the sectors are orange, two of the sectors are yellow, and one sector is green. Landing on the green sector will give 3 points, landing on the yellow sector will give 1 point; landing on an orange sector will give 0 points, and landing on a pink sector will give -1 point. Let x = the points you have after one spin a. Construct a probability distribution b. If you take one spin, what is your expected value? c. 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.

1. A game at thefair involves a wheel with seven sectors. Two of the sectors are pink, two of the sectors are orange, two of the sectors are yellow, and one sector is green.

Landing on the green sector will give 3 points, landing on the yellow sector will give 1 point; landing on an orange sector will give 0 points, and landing on a pink sector will give -1 point.

Let x = the points you have after one spin

a. Construct a probability distribution

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

c. 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.