Neighbor asked:


Mega Millions tickets cost $1 per play. Players may pick six numbers from two separate pools of numbers: five different numbers from 1 to 56, and one number from 1 to 46. You win the jackpot by matching all six winning numbers in a drawing. According to the Illinois Lottery website, the chances of winning are given in the table.

Match White Match Gold Prize Chances
5 1 Jackpot 1 in 175,711,536
5 0 $250,000 1 in 3,904,701
4 1 $10,000 1 in 689,065
4 0 $150 1 in 15,313
3 1 $150 1 in 13,781
2 1 $10 1 in 844
3 0 $7 1 in 306
1 1 $3 1 in 141
0 1 $2 1 in 75

Right now the jackpot is worth $12 million. If you buy a ticket, what is the expected value?

How much would the jackpot have to be for the expected value to be more than $0? (Assume that you were the only one to choose the winning numbers)

Floyd