4.33 Winning the lottery. A state lottery’s Pick 3 game asks players to choose a three-digit number, 000 to 999. The state chooses the winning three-digit number at random so that each number has probability 1/1000. You win if the winning number contains the digits in your number, in any order.
(a) Your number is 059. What is your probability of winning?
(b) Your number is 223. What is your probability of winning?