To accurately simulate the tennis match between Jim and Rob using a number cube (which has numbers 1 to 6), we need to ensure that the associations represent the probability of winning each game in a way that reflects the evenly matched nature of the players. Specifically, we want equal probabilities of winning for both players, which means each player should have an equal number of outcomes on the cube.
Let's analyze each option:
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Number 1 on the cube represents Jim, and number 3 represents Rob.
- This association gives Jim a 1/6 chance of winning (only the outcome '1') and Rob a 1/6 chance (only the outcome '3'). The remaining outcomes (2, 4, 5, 6) are not accounted for. This doesn't evenly match the players. Not valid.
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Even numbers on the cube represent Jim, and odd numbers represent Rob.
- Even numbers are 2, 4, and 6 (3 outcomes), while odd numbers are 1, 3, and 5 (3 outcomes). This is an even distribution. Valid.
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Numbers 1, 3, 4, and 5 represent Jim, and numbers 2 and 6 represent Rob.
- Jim has 4 outcomes (1, 3, 4, and 5), while Rob has 2 outcomes (2 and 6). This does not provide an even match. Not valid.
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Odd numbers on the cube represent Jim, and even numbers represent Rob.
- Odd numbers are 1, 3, and 5 (3 outcomes), and even numbers are 2, 4, and 6 (3 outcomes). This is an even distribution. Valid.
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Numbers 2 and 3 represent Jim, and numbers 1, 5, 4, and 6 represent Rob.
- Jim has 2 outcomes (2 and 3), while Rob has 4 outcomes (1, 4, 5, and 6). This does not provide an even match. Not valid.
In summary, the valid associations on the cube that accurately simulate the situation are:
- Even numbers on the cube represent Jim, and odd numbers represent Rob.
- Odd numbers on the cube represent Jim, and even numbers represent Rob.