At a raffle, 1500 tickets are sold for $2 each for four prizes of $500, $250, $150, and $75. You buy one ticket. What is the expected value of your gain?

To find the expected value of your gain in each prize, subtract the price of the ticket from the prize:

If the prize is $500: $500 - $2 = $498

If the prize is $250: $250 - $2 = 248

If the prize is $160: $160 - $2 = $73

But if you did not win any cash prize, you do not have any gain because

0 cash prize - $2 ticket = - $2 which is a loss