A carnival operator is constructing a new game.
In this game, the player will place a bet. Then a ball is selecteded from an urn containing balls of three colours: 2 green balls, 4 red balls and 7 white balls.
If a red ball is drawn, the player wins 3$, if a green ball is drawn, the player wins 4$, and if a white ball is drawn the player wins nothing.
What should the carnival operator set the bet at such that on average he makes $0.50 profit a game? (That is, so the player loses $0.50)