To play the Mega Millions Louisiana Lottery consists of picking five numbers from 1 to 75 and one yellow Mega Ball number from 1 through 15. (You can play up to five different sets of numbers on each playslip but we will just assume one play per ticket to keep things straight.) Each play costs $1 and you can pay an additional $1 to apply a "multiplier" which multiplies any non-Jackpot prize by the Multiplier number (2, 3, 4, or 5) randomly selected at the time of the drawing.

On October 10, 2016 the jackpots listed were

Match 5 plus Mega ball = Jackpot of $49,000,000 with cash value of $32,600,000
Match only 5 = $1,000,000
Match 4 plus Mega ball = $5,000
Match only 4 =$500
Match 3 plus Mega ball = $50
Match only 3 = $5
Match 2 plus Mega ball = $5
Match 1 plus Mega ball = $2
Match only the Mega ball = $1

Verify the posted odds

Match 5 plus Mega ball = 1 in 258,890,850
Match only 5 = 1 in 18,492,204
Match 4 plus Mega ball = 1 in 739,688
Match only 4 = 1 in 52,835
Match 3 plus Mega ball = 1 in 10,720
Match only 3 = 1 in 766
Match 2 plus Mega ball = 1 in 473
Match 1 plus Mega ball = 1 in 56
Match only the Mega ball = 1 in 21

Determine the expected payout for each ticket purchased. Also, determine what the Jackpot would need to be in order for the game to be considered "fair" with an expected value of zero.

Solution.