Question: You are thinking about playing a lottery. The rules: you buy a ticket, choose 3 different numbers from 1 to 100 and write them on the ticket. The lottery has a box with 100 balls numbered 1 to 100. Three balls are drawn at random without replacement. If the numbers on these balls are the same as the numbers on this ticket in any order, you win. The balls do not have to be drawn in the order on your card.

a) If you decide to play, what is your chance of being a winner?

b) It costs $1 to buy a ticket. If you match the 3 numbers as described above, you win $20,000. What are your expected net-winnings each time you buy one ticket? (Note: your net winnings are $-1 when you lose and $19,999 since the lottery gets to keep the $1 you paid for the ticket even when you win).