Given the payoffs, compute the expected value for this game.

Question

A game consist of tossing one dart at the dartboard, which has the values of Win $12, Lose $9, and Win $6. Assume the dart  hits one of these. Given these payoffs,compute the expected value for this game. Express in $ and cents and show all work.

The answer is lose $0.50 but I can't figure out how it is.

Answer 1

Suppose the probability of hitting win $12 is a, the probability of hitting lose $9 is b and the probability of hitting win $6 is c.

The expected value is 12a - 9b + 6c, which should give you -0.5