Many states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery from the Tri-State Pick 3 game that New Hampshire shares with Maine and Vermont. You choose a three-digit number; the state chooses a   three-digit winning number at random and pays you $500 if your number is chosen. If your ticket costs $1, what is your expected value for this lottery?

Question
Asked Nov 22, 2019
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Many states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery from the Tri-State Pick 3 game that New Hampshire shares with Maine and Vermont. You choose a three-digit number; the state chooses a   three-digit winning number at random and pays you $500 if your number is chosen. If your ticket costs $1, what is your expected value for this lottery?

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Expert Answer

Step 1

The possible three digit numbers varies from 000 to 999 making a total of 1000 numbers.

Consider X be the amount your ticket pays you. Therefore, the probability distribution of X is,

Payoff X
Probability 1/1000 0.001 1-(1/1000) = 0.999
$500
$0
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Payoff X Probability 1/1000 0.001 1-(1/1000) = 0.999 $500 $0

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Step 2

The random variable X is 500 if the selected number is equal to the one that you ch...

E(X) $500 (0.001) + $0 (0.999)
-$0.50
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E(X) $500 (0.001) + $0 (0.999) -$0.50

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