Question

In a lottery, 5000 tickets are sold for $1 each, one first prize of $2000, 1 second prize of $500, 3 third prizes of $100, and 10 consolation prizes of $25 are to be awarded. What are the expected net earnings of a person who buys one ticket?

Answer 1

There is 1/5000 chance to win first place of $2000,
1/5000 chance to win second place of $500
3/5000 chance to win third place of $100
10/5000 chance to win the consolation prize of $25.
The ticket costs $1.
We multiply each probability by the amount, and subtract the ticket cost, to get the expected net earnings:
(1/5000)($2000) + (1/5000)($500) + (3/5000)($100) + (10/5000)($25) - $1 = $(-0.39).
This means that there is an expected loss of $0.39.