Posted by **Stephanie** on Sunday, December 7, 2008 at 9:08pm.

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?

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