SUPPOSE YOU BUY 1 TICKET FOR $1 OUT OF A LOTTERY OF 3000 TICKETS. IF THE PRIZE FOR THE ONE WINNING TICKET IS TO BE $500, WHAT ARE YOUR EXPECTED WINNINGS?
expected value=500*1/3000=.17cts
To calculate your expected winnings, you need to multiply the probability of winning by the amount you could potentially win, and then subtract the cost of buying the ticket.
First, let's calculate the probability of winning. Since there is only one winning ticket out of a total of 3000 tickets, the probability of winning is 1/3000.
Next, we multiply the probability of winning by the amount you could potentially win. In this case, the potential winnings are $500.
(1/3000) * $500 = $0.1667
So, your expected winnings are $0.1667.
Note that this means, on average, if you were to play this lottery many times, you would expect to lose money since your expected winnings are less than the cost of the ticket.