Keno Keno is a favorite game in casinos, and similar games are popular with the states

Chapter 6, Problem 9

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QUESTION:

Keno 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 Mark 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. Let X = the net amount you gain on a single play of the game. (a) Make a table that shows the probability distribution of X. (b) Compute the expected value of X. Explain what this result means for the player.

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QUESTION:

Keno 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 Mark 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. Let X = the net amount you gain on a single play of the game. (a) Make a table that shows the probability distribution of X. (b) Compute the expected value of X. Explain what this result means for the player.

ANSWER:

Step 1 of 4

Given,

Number of balls = 80

Number of balls chosen at random = 20.

Playoff on $1 bet  = $3

Probability of winning =

Let the net amount you gain on a single play of the game be denoted as X. We have to determine the following:

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