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 XProbability -$999,9980.0000006 -$980.008 -$80.02 $21-(.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.