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.

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Presentation transcript:

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

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

The values of x and its probability XProbability -$999, $ $80.02 $21-( ) = E(X) = (-999,998)( )+(-98)(0.008)+(- 8)(0.02)+2( )= $0.40

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.