To determine the correct responses regarding the probabilities of different outcomes when rolling a six-sided die, let's analyze each statement:
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A. Probability of an even number is \( \frac{1}{2} \)
- The even numbers on a six-sided die are 2, 4, and 6.
- There are 3 even numbers, so the probability is \( \frac{3}{6} = \frac{1}{2} \).
- This statement is correct.
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B. Probability of a 1 or 5 is \( \frac{1}{3} \)
- The numbers that are either 1 or 5 are just 1 and 5.
- There are 2 favorable outcomes, so the probability is \( \frac{2}{6} = \frac{1}{3} \).
- This statement is correct.
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C. Probability of a number less than 3 is \( \frac{1}{2} \)
- The numbers less than 3 on a six-sided die are 1 and 2.
- There are 2 favorable outcomes, so the probability is \( \frac{2}{6} = \frac{1}{3} \).
- This statement is incorrect.
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D. Probability of a 2 or an odd number is
- The odd numbers on a six-sided die are 1, 3, and 5, plus the even number 2.
- The outcomes are 1, 2, 3, and 5. This gives us 4 favorable outcomes.
- The probability is \( \frac{4}{6} = \frac{2}{3} \).
- This statement is correct.
In summary, the correct responses are A, B, and D.