20.15 Keno. Keno is a popular game in casinos. Balls numbered 1 to 80 are tumbled in a machine as the bets are placed, then 20 of the balls are chosen at random. Players select numbers by marking a card. Here are two of the simpler Keno bets. Give the expected winnings for each.
(a) A $1 bet on “Mark 1 number” pays $3 if the single number you mark is one of the 20 chosen; otherwise, you lose your dollar.
(b) A $1 bet on “Mark 2 numbers” pays $12 if both your numbers are among the 20 chosen. The probability of this is about 0.06. Is Mark 2 a more or a less favorable bet than Mark 1?