Most states and Canadian provinces have government-sponsored lotteries. Here is

Question

Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery wager, from the Tri-State Pick 3 game that New Hampshire shares with Maine and Vermont.   You choose a 3-digit number, 000 to 999. The state chooses a three-digit winning number at random and pays you $500 if your number is chosen.    b)    What is the standard deviation for the payoff? (10 pts.) Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery wager, from the Tri-State Pick 3 game that New Hampshire shares with Maine and Vermont.   You choose a 3-digit number, 000 to 999. The state chooses a three-digit winning number at random and pays you $500 if your number is chosen.    b)    What is the standard deviation for the payoff? (10 pts.)

Explanation / Answer

Probability of winning =p= No. of chances of winning /Total number of chances = 1/1000

Probability of loss = 1-p = 999/1000

Payoff at win =500

Payoff at loss = 0

Mean payoff = 1/1000*500+999/1000*0 = 0.5

Variance = 1/1000 [ 500-0.5]^2 + 999/1000 [ 0-0.5]^2 = 249.75

Standard deviation = sqrt(variance) = sqrt(249.75) = 15.803

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