Question

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.

(Use decimal notation. Give your answers as exact numbers.)
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.
expected winnings: $___

Answer 1

The expected winnings for a $1 bet on "Mark 1 number" in Keno are $0.25, based on the probability of the chosen number being drawn and the payout for winning.

Step-by-step explanation:

The expected winnings for a $1 bet on "Mark 1 number" in Keno can be calculated using the probability of winning. Since there are 80 numbers and 20 are drawn, the chance that the single number you mark is drawn is 20/80 or 1/4. If you win, you get $3 in addition to your $1 bet, so the total return is $4. Therefore, the expected winnings are:

(Probability of Winning) x (Winning Amount) + (Probability of Losing) x (Losing Amount)

Expected winnings = (1/4) x $4 + (3/4) x (-$1) = $1 - $0.75 = $0.25

Thus, if you bet $1 on "Mark 1 number," your expected winnings are $0.25.