The Lottery is offering a new Super Scratchers lottery ticket starting next year. Each ticket costs $2.00 to purchase. The odds for winning are given below. Answer the following questions based on this information and be sure to explain the steps you used to arrive at your answers:

Amount
Odds of Winning
$1.00 = 1 in 20
$2.00 = 1 in 40
$4.00 = 1 in 80
$5.00 = 1 in 100
$10.00 = 1 in 200
$15.00 = 1 in 500
$25.00 = 1 in 2,000
$50.00 = 1 in 4,000
$100.00 = 1 in 10,000
$200.00 = 1 in 20,000
$1000.00 = 1 in 40,000

1. What is the probability (as a percentage) of not winning anything?

2. What is the expected value of each Super Scratcher ticket?

3. Assume you spend $200,000 on Super Scratcher tickets. How much money do you think you would expect to win?

4. Let’s say the Lottery decides to promote their new ticket by offering a Super Duper Scratcher ticket the first month of sales that includes a chance to win $100,000 dollars with 1 in 40,000 odds of winning. Assuming none of the other winning odds change, is this a better or worse expected value per ticket? Explain your answer.