Circles & Lines · Medium problem

A game costs $\$5$ to play. A player draws one ball from a bag containing $3$ red, $2$ blue, and $1$ gold ball, all equally likely. A red ball pays $\$2$, a blue ball pays $\$6$, and a gold ball pays $\$x$. For what value of $x$ is this game exactly fair, meaning the expected payout equals the $\$5$ cost to play?