Imagine you are in a game show. There are 20 prizes hidden on a game board with 100 spaces. One prize is worth $50, nine are worth $20, and another ten are worth $10. You have to pay $5 to the host if your choice is not correct. Let the random variable x be the money you get or lose. Show all work. Just the answer, without supporting work, will receive no credit.
(a) Complete the following probability distribution.
x P(x) -$5 $10 $20 $50
(b) What is your expected winning or loss in this game? Be specific in your answer whether it's winning or loss.