Asked by Stephanie

4.34 Keno is a favorite game in casinos, and similar games are popular with the
states that operate lotteries. 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. The simplest of the many wagers available is marking
1 number." Your payoff is $3 on a $1 bet if the number you select is one of those
chosen. Because 20 of 80 numbers are chosen, your probability of winning is 20/80,
or 0.25.
(a) What is the probability distribution (the outcomes and their probabilities) of
the payoff X on a single play?
(b) What is the mean payoff X?
(c) In the long run, how much does the casino keep from each dollar bet?

Answered by economyst
In the simple KENO game where one number is played.

a) There is a 25% chance of winning $3 and a 75% chance of winning zero.

b) the mean payoff is .25*3 + .75*0. = 0.75 or 75 cents on each dollar bet.

c) from b, the casino keeps 25 cents on each dollar bet.
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