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A particular state has a lottery game which consists of choosing five digits, each one from 0 thru 9, with repetitions allowed. The winning
number is determined by randomly selected ping-pong balls from each of five vats with balls numbered 0 thru 9:
Prizes are awarded for the following:
\circ If all five numbers match -- i.e., you have a match in every place -- you win $25,000.
\circ If you have a match in exactly four of five places, you win $1,000
\circ If you have a match in exactly three of five places, you win $10
\circ Two matches or fewer wins you nothing
Lottery tickets cost $1. Let $X$ = the amount of money that a ticket holder wins. Find the expected value of $X$. What does this tell you about
how much the lottery commission profits on every dollar they take in? (You have to find the expected value the \text{``long way''})
