simple probability exercise

[marbles]

This one might be a little fun for the guys that are more of beginners in probability theory:

All numbers can be found at the "instant games" section of wilottery.com.

For a current scratch-off game, the wisconsin lottery gives the following odds of winning:

$1 1:10
$2 1:10
$10 1:55
$25 1:400
$50 1:400
$100 1:89,143
Grand prize 1:520,000

Question 1: If the Expected return on a $1 ticket is 67.42 cents (or an E.V. of -32.58 cents, if you prefer), what is the payout for the grand prize?

Question 2: The site gives the odds of "winning" (payout greater than zero) as approximately 1:4.5. What are the odds of returning a profit on a $1 ticket?

Question 3: What is the expected return on a ticket, given that you know it's a "winner" (payout greater than zero)? Hint: you'll need to solve question 1 first.

solutions later.