At a carnival, a toy boat race costs $4 to enter. Second place earns a prize worth $8, and third place earns a prize worth $5. If the probability of winning any of the prizes is [tex]\frac{1}{12}[/tex], what should the first place prize be worth for the game to be fair?



(a) $35


(b) $23


(c) $31


(d) $41