A lottery has the following three prizes and sells 2 million tickets
1) one bumper prize of 1 million dollars.
2) 100 first prizes of 10,000 dollars each.
3) 10,000 consolation prizes of 1 dollar each.
If one ticket costs 2 dollars, should you buy the ticket?
The answer to this question depends on two aspects.
A) The difference between the expected value and cost of a single ticket.
B) The risk appetite of the buyer.
Expected value of a ticket
EV = P(1,000,000) x 1,000,000 + P(10,000) x 10,000 + P(1) x 1
where P(1,000,000) is the probability of winning a million dollar = 1 / 2,000,000
EV = [1/2,000,000] x 1,000,000 + [100/2,000,000] x 10,000 + [10,000/2,000,000] x 1
= 1.005
The cost of a ticket ($2) is higher than the expected value of winning ($1). A risk-averse or a risk-neutral person would avoid it.
