A lottery has a grand prize of 160000 four runnerup prize of

A lottery has a grand prize of $160,000, four runner-up prize of $32,000 each, seven third-place prizes of $8000 each, and twelve consolation prizes of $400 each. If 640,000 tickets are sold for $1 each and the probability of any one ticket winning, find the expected net winnings on a $1 ticket.

Solution

Expected return = Total return / Number of tickets

Total return = [160,000 + 4(32000) + 7(8000) + 12(400)] = 348800

348,800 / 640,000 = .545

Expected return on a $1.00 ticket is $0.55