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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?

• stats: need help please -

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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