what is the Expected Value

Question

Tickets for a raffle cosr 19. There were 721 tickets sold. One ticket will be randomly selected as the winner, and that person wins 1300 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?

Answer 1

There is a 1/721 chance of winning $1300. There is a 720/721 chance of losing $19

The expected winnings from the raffle are (1/721)($1300) + (720/721)(-$19) = ($1.80)+(-$18.97)

Multiply simplify and that equals close to an expected value of a ticket as negative $17.17 Your

expected loss is $17.17 for buying one ticket.

720 people together pay out $19 x 720 = $13,680 for tickets. The raffle promoters keep $12,380 as their profit

and pay out $1300 to the winning ticket holder. The other losing ticket holders together lost

720($-17.17)=$12,362= $19 less than the profit of the raffle promoters.

There may be a slight rounding error in these calculations, but it should be within a dollar or so. It's not a very

good bet to buy a ticket. It's an even worse bet to buy more than one ticket. The more tickets you

buy the more you expect to lose. Your odds of winning are far better in lotteries or casinos.