Tickets for a raffle cost $14.

Question

Tickets for a raffle cost $14. There were 728 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1700 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. Express the answer rounded to two decimal places.

Answer 1

The expected value takes into account all the possible outcomes and determines a weighted average of all of them. For example,suppose I roll a fair six-sided die and you bet one dollar on the outcome, and I agree to payout 3 dollars if you guess correctly, otherwise I keep your dollar. In this case there is one way for you to get a 3 dollar payout, and five ways for you to lose a dollar for the six possible outcomes. If all six possibilities occur (let's say we played 6 times) then you were paid 3 dollars once, but I kept 1 dollar five times, and you had a net loss of two dollars. Divide that by the numbers of times we played for the expected value of -$0.33. In other words, you would be expected to lose 33 cents each time you played. Pretty good for me.

Mathematically this would be Payout(probability of winning) - Cost to play(probability of losing)

Applying this to the raffle, each ticket costs 14 dollars, 728 tickets are sold, and the payout is 1714 dollars. Plug those numbers into the formula and we have:

1714(1/728) - 14(727/728) = -8464/728 = -$11.62