If the PowerBall lottery has $100 million prize, and tickets cost $1.00 each, and there are 500 million tickets sold, what is the expected value of each ticket? Is it rational to purchase a ticket? What if you know that only 50 million tickets have been sold? Explain why, if people tend to use their childrens' birthdays when selecting numbers to play on the "Pick Three" lottery, you might be better off using the last six digits of your Social Security number.