Question

point) A charity holds a raffle in which each ticket is sold for $30. A total of 10800 tickets are sold. They raffle one grand prize which is a Mercedes Benz E350 valued at $55000 along with 5 second prizes of Honda motorcycles valued at $8000 each. What are the expected winnings for a single ticket buyer?  Express to at least three decimal place accuracy in dollar form (as opposed to cents).
Answer: $

Answer 1

Total number of tickets sold = 10800

Price of each ticket = $30

First prize = $55000

P[ first prize ] = 1/10800

Second Prize = $8000

P[ second prize ] = 5/10800

Expected winnings for a single ticket buyer = First prize*P[ first prize ] + Second Prize*P[ second prize ] - Price of each ticket

Expected winnings for a single ticket buyer = 55000*(1/10800) + 8000*(5/10800) - 30

Expected winnings for a single ticket buyer = 55000/10800 + 40000/10800 - 30

Expected winnings for a single ticket buyer = 5.092 + 3.704 - 30

Expected winnings for a single ticket buyer = 8.796 - 30

Expected winnings for a single ticket buyer = -$21.204