A dice game involves throwing three dice and betting on one of the six numbers that are on the dice. The game costs$1to play, and you win if the number you bet appears on any of the dice. The distribution for the outcomes of the game (including the profit) is shown below:

Number of dice with your number Profit Probability of Observing -$1 125/216 $1 75/216 $3 15/216 $3 1/216