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Lottery Problem

Lottery Problem. A state run monthly lottery can sell 100,000tickets at $2 a piece. A ticket wins $1,000,000with a probability 0.0000006, $100 with probability 0.008 and $10 with probability 0.02. On an average how much can the state expect to profit from the lottery per month?

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Lottery Problem

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  1. Lottery Problem A state run monthly lottery can sell 100,000tickets at $2 a piece. A ticket wins $1,000,000with a probability 0.0000006, $100 with probability 0.008 and $10 with probability 0.02. On an average how much can the state expect to profit from the lottery per month? What random variable does X represent?

  2. Let X be the random variable that gives the net profit to the state on a single ticket. Therefore X takes the values ($2-$1,000,000) = -$999,998 ($2-$100) = -$98 ($2-$10) = -$8 $2

  3. The values of x and its probability X Probability -$999,998 0.0000006 -$98 0.008 -$8 0.02 $2 1-(.0000006+.008+.02) = 0.9719994 E(X) = (-999,998)(.0000006)+(-98)(0.008)+(-8)(0.02)+2(0.9719994)= $0.40

  4. conclusion We see that the average profit to the state for a $2.00 ticket is $0.40 If the state sells 100,000 tickets it can expect an average monthly profit of ($0.40)(100,000) = $40,000.

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