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Probability played a role in the rigging of the April 24, 1980, Pennsylvania state lottery. To determine each digit of the three-digit winning number, each of the numbers 0, 1, 2, , 9 was written on a Ping-Pong ball, the 10 balls were blown into a compartment, and the number selected for the digit was 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. They then proceeded to buy lottery tickets bearing the potential winning numbers. How many potential winning numbers were there (666 was the eventual winner)?

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Answer:

8 potential winners ( 444, 446, 644, 464, 466, 646, 664, 666)

Step-by-step explanation:

To alter the odds the balls numbered 4 and 6 werent injected with liquid and hence they will float making it certain for their selection and determination as the winning digits. The potential of the winning numbers are (2)^3=8.

Since 4 and 6 ain't filled with liquid, they would be selected and determine the digits in the winning numbers in 8 ways ( 444, 446, 644, 464, 466, 646, 664, 666). The potential winning number is among them.

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