The Governor for the State of Alabama is considering starting a weekly lottery to help raise money for the state. The Governor's buddies have devised a game where participants must pick six numbers from a set of possible winning numbers. The more winning numbers the participant picks correctly, the greater the prize. The cost to participants is $1 for each entry into the game. On the back of each ticket is the following information regarding the probability of winning specific amounts of cash. Numbers Matched Prize x Probability P(x) 1 $1 0.4130195 2 $10 0.132378 3 $100 0.0176504 4 $1,000 0.0009686 5 $10,000 0.0000184 6 $100,000 0.0000001 Note the following: The $1 fee to play the game is a sunk cost for the contestant. That is, regardless of how many, if any, numbers the contestant matches, the contestant does not get the $1 back. In the case of the contestant matching 2 numbers, the contestant pays $1 to play and wins $10, so the contestant's net