Probability played a role in the rigging of the 24-April-1980 Pennsylvania state lottery (Los Angeles Times, 8 September 1980). To determine each digit of the three-digit winning num-ber, each of the numbers 0, 1, 2, ..., 9 is placed on a Ping-Pong ball, the ten balls are blown in-to a compartment, and the number selected for the digit is the one on the ball that floats to the top of the machine. To alter the odds, the conspirators injected a liquid into all balls used in the game except those numbered 4 and 6, making it almost certain that the lighter balls would be selected and determine the digits in the winning number. Then they bought lottery tickets bearing the potential winning numbers.
1. How many potential winning numbers were there (666 was the eventual winner)?
2. What would have been the probability of the winning number being one of the potential winning numbers had there been no rigging of the lottery?