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Chapter 6: Q.9 (page 354)

Keno is a favorite game in casinos, and similar games are popular in the states that operate lotteries. Balls numbered 1to 80are tumbled in a machine as the bets are placed, then 20of the balls are chosen at random. Players select numbers by marking a card. The simplest of the many wagers available is 鈥淢ark 1Number.鈥� Your payoff is 3on a bet if the number you select is one of those chosen. Because 20of 80numbers are chosen, your probability of winning is 20/80, or 0.25. Let X=the 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

Short Answer

Expert verified

a)Thus the probability distribution is

X(S)
-1
2
probability0.75
0.25

b)The expected value is-0.25

Step by step solution

01

Part(a) Step 1: Given Information

The probability of winning the game is 0.25.

The amount of bet is 1.

The payoff for the game is 3.

02

Part (b) Step 2: Calculation

The reward is 3in this case. If the game is won, the payout reduces the stake. To put it another way,

payoff=3-1=2

The probability distribution is calculated using the information provided.

X(S)-12Probability1-0.250.75

03

Part (b) Step 1: Given Information 

Probability of wining the game is0.25.

Amount of bet is1.

Payoff for the game is$3.

04

Part (b) Step 2: Calculation 

The expected value can be calculated as:

E(X)=鈭�x脳P(x)=鈭�1(0.75)+(2)(0.25)=-0.25

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