Keno is a lottery-type gambling game where players pay to choose a certain amount of integers from 1 to 80. Each selection is called a "spot." After the players have make their bet, the house randomly picks 20 of these 80 integers. The payoff for each player is depended on how many of their chosen number matches with the 20 numbers from the house. Each match is called a "hit," and the more hits the players get, the higher their payoff will be.
- Suppose you pay $1 to mark one spot (number). If your chosen number is a hit, you win $3. Otherwise, you lose that $1. What is your expected/average payoff in this game?
- Suppose you spend $1 to mark two spots (numbers). If the house hits both of your numbers, you win X dollar(s). Otherwise, you lose that $1. What should X be for the expected payoff to be zero (fair game)?
Please explain step by step in detail.