Answer for problem #7:

To coerce more people into purchasing a ticket, I would introduce an additional chance of winning. Any tickets with the same first 3 digits of the grand prize ticket will receive a $20 consolation prize. I would also lower the ticket price from $8 to $7 to slightly increase the player's net gain. Additionally, 500 more raffle tickets will be added to the total assuming once the total profit for the raffle would sum up to be $4910.

23000(7)= $210009(9) + 100(30)+ 500(10)+ 8000(1)

= $160902100-16090

-$4910

Current Problem #8:

Construct a new probability distribution describing the net gain (from the player's perspective) for the game with your proposed changes from #7.