Many lottery games for very large prices include guessing which numbers will appear from a random sample of the numbered balls. In Minnesota's Gopher 5 lottery, there are five balls numbered 1-47. If a player matches at least two balls, She wins a prize( see table below). If the cost of playing is one dollar, how large must the jackpot be before The expected return of playing Gopher 5 becomes favorable to the player? Assume there is only one winner, and also ignore the fact that winnings are also taxed.

Table:

Match. Win. Odds.

5 of 5. Jackpot 1 in 1,533,939

4 of 5. $500. 1 in 7,304

3 of 5 $15. 1 in 178

2 of 5 $1. 1 in 13