Probability played a role in the rigging of the April 24, 1980, Pennsylvania state lottery (Los Angeles Times, September 8, 1980). To determine each digit of the three-digit winning number, 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 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. How many potential winning numbers were there (666 was the eventual winner)?
Answer:
There were 8 potential winning numbers
Step-by-step explanation:
According on what the exercise says, there are 2 numbers likely to be selected in each of the 3 rolls: 4 and 6. Since we are picking 3 digits, and each digit give us 2 possibilities, then we have a total of 2³ = 8 potential winners (namely 444, 446, 464, 644, 466, 646, 664 and the winner 666).
Final answer:
With only the numbers 4 and 6 being unaltered in the rigged Pennsylvania state lottery, there were 8 potential winning combinations calculated by the possible arrangements of these two numbers in a three-digit sequence.
Explanation:
In the case of the rigged Pennsylvania state lottery on April 24, 1980, with the numbers 4 and 6 being the only ones not manipulated to be heavier, the potential winning numbers would have been all combinations of 4 and 6 for the three-digit number. Since each position in the three-digit number could be either a 4 or a 6, we have 2 choices for the first digit, 2 choices for the second digit, and 2 choices for the third digit.
Calculating the total number of potential winning combinations gives us:
2 choices x 2 choices x 2 choices = 8 potential winning numbers.
Thus, there were 8 potential winning numbers, with 666 (which consists exclusively of the untampered balls numbered 6) being the eventual winner.
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