A carnival operator is constructing a new game.
In this game, the player will place a bet. Then a ball is selected from an urn containing balls of three colours: $2$ green balls, $3$ red balls and 5 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 $\$0.50$)