Consider a lottery game in which there is an 80% chance of winning nothing, 10% chance of winning $1, 9% chance of winning $100, and 1% chance of winning $100,000.

Explain mathematically: If the tickets cost $5, as a player would it be financially prudent to play? If, as the lottery operator, you had the ability to reduce the value of the last probability i.e. the probability P(X = $100,000), then adjust P(X= 0) accordingly, and could raise the price to $10, could this lottery be profitable?