What are the expected​ winnings?

Question

A raffle offers a first prize of $1000, 2 second prizes of $300, and 20 third prizes of $10 each. If 20000 tickets are sold at 75 cents each, find the expected winnings for a person buying 1 ticket.

Answer 1

1000(1/20000) +

300(2/20000) +

10(20/20000) +

=

 

1800/20000 = .09

 

Each ticket purchased is expected to win 9 cents

 

Each ticket purchased cost 75 cents

 

If you interpret expected winnings per ticket to include the cost then each ticket is expected to lose 66 cents. 

Answer 2

probability of winning first prize = p1 = 1/20000

probability of winning a 2nd prize = p2 = 2/20000 = 1/10000

probability of winning a 3rd prize = p3 = 20/20000 = 1/1000

E = expectation value = Sum_i=1..3 pi * Vi, Vi = value of prize, pi = probability of winning prize,

E = 1/20000*1000 + 1/10000*300 + 1/1000*10 = 1/20 + 3/100 + 1/100 = 9/100 = 9 cents = expected winnings for a person buying one ticket.