Let's evaluate each response regarding the outcomes of rolling a six-sided die, where the possible outcomes are {1, 2, 3, 4, 5, 6}.
A. Probability of an even number: The even numbers on a six-sided die are 2, 4, and 6. There are 3 even numbers.
- Probability of rolling an even number = Number of even outcomes / Total outcomes = 3/6 = 1/2.
- This statement is correct.
B. Probability of a 1 or 5: The outcomes for a 1 or 5 are simply the numbers 1 and 5. There are 2 outcomes.
- Probability of rolling a 1 or a 5 = Number of outcomes (1 or 5) / Total outcomes = 2/6 = 1/3.
- This statement is correct.
C. Probability of a number less than 3: The numbers less than 3 are 1 and 2. There are 2 outcomes.
- Probability of rolling a number less than 3 = Number of outcomes (1 and 2) / Total outcomes = 2/6 = 1/3.
- This statement is incorrect.
D. Probability of a 2 or an odd number: The odd numbers on a six-sided die are 1, 3, and 5. Adding 2 gives us these outcomes: 1, 2, 3, and 5. There are 4 outcomes (1, 2, 3, 5).
- Probability of rolling a 2 or an odd number = Number of outcomes (1, 2, 3, 5) / Total outcomes = 4/6 = 2/3.
- This statement is correct.
Summary:
- A is correct: Probability of an even number is \( \frac{1}{2} \).
- B is correct: Probability of a 1 or 5 is \( \frac{1}{3} \).
- C is incorrect: Probability of a number less than 3 is \( \frac{1}{3} \) (not \( \frac{1}{2} \)).
- D is correct: Probability of a 2 or an odd number is \( \frac{2}{3} \).
The correct responses are A, B, and D.