1) Explain the differences between an observation and an inference. Relative to what "probability" means, how does this difference affect your definition of probability?
2) Consider the scenario detailed:
To determine each digit of the three-digit winning number in the Pennsylvania state lottery, each of the numbers 0, 1, 2, ..., 9 is placed on a Ping-Pong ball, the ten balls are blown into 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 expect those numbered 4 and 6, making it almost certain that the lighter balls would be selected and determine the winning number. Then they bought lottery tickets bearing the potential winning numbers.
Discuss what could have gone wrong (from a probability standpoint) with this type of game-fixing. How confident should the conspirators have been that this plan would work? Does the selection of any of the numbers affect the selection chances of the other two numbers, and explain your reasoning.