# A charity raffle has one $1000 prize, three $250 prizes and ten $5 prizes. A total of 500 tickets are sold at $5 each. What is the expected profit per ticket?

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Expert Answers

degeneratecircle | Certified Educator

The probability of winning $1000 is 1/500, the probability of winning $250 is 3/500, and the probability of winning $5 is 10/500. By definition, the expected value of a ticket is then

`1/500($1000)+3/500($250)+10/500($5)=$1800/500=$3.60.`

The cost of a ticket is $5, so the expected profit of a ticket is

`$5-$3.60=-$1.40,` or in other words, you can expect to lose $1.40 if you buy a ticket.

While you expect to lose $1.40, the charity expects to gain $1.40. So from their point of view, the profit is $1.40, not -$1.40.