To play pick 3, you choose any three digits between 0 and 9 (repetitions are allowed). The order you select them in is important. You then get to select the "play type" (or the game) you wish to use with your three numbers.

a.) How many possible numerical outcomes are there to the Pick 3 Lottery?

b.) If you play $1 straight, what is the expected value of this game (round to the nearest cent)? (Note that the prize does not take into account that you already paid $1 for the ticket.)

c.) If you play $1 box where your number has 3 different digits, what is the expected value of this game?

d.) If you play $1 Front Pair, what is the expected value of this game?

e.) If you were to buy $100 worth of Pick 3 tickets, What is the maximum amount of money you could have won? What is the minimum amount of money you could have won? How much money would you expect to win/lose? How much of your original $100 would you still expect to have?

f.) Is this game worth playing? Justify your answer.