Question

Tickets for a raffle cost $12. There were 756 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1500 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)?

If the Expected Value is negative, be sure to include the "-" sign with the answer.

Answer 1

Most likely $2 but possibly $-9.98.

Explanation:

Since there are 756 tickets sold, there is a 1/756 chance that a ticket-buyer will win the prize, and a 755/756 chance that a ticket-buyer will not.

The expected value of their winnings will then be (1/756)(12+1500) + (755/756)(0) = $2.

However, if the winnings are interpreted as -12 if no prize is won, the expected value would then be (1/756)(12+1500) + (755/756)(-12) = $-9.98.