A fair die ( 6 sided) is rolled. Express the answers in simplest fraction form. P(even *) = \( P( \) multiples of 2\( )= \) \( P( \) odd \( \#)= \) \( P( \) multiples of 4\( )= \) \( P(2 \) or 3\( )= \) \( P(7)= \) \( P(5)= \) \( P(2 \) or higher \( )= \)

Let's analyze each probability for a fair 6-sided die with outcomes \( \{1, 2, 3, 4, 5, 6\} \). Each outcome has an equal probability of \( \frac{1}{6} \). 1. **\( P(\text{even}) \)** **Even numbers:** 2, 4, 6 \[ P(\text{even}) = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} \] 2. **\( P(\text{multiples of 2}) \)** Multiples of 2 are the even numbers: 2, 4, 6 \[ P(\text{multiples of 2}) = \frac{3}{6} = \frac{1}{2} \] 3. **\( P(\text{odd}) \)** **Odd numbers:** 1, 3, 5 \[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \] 4. **\( P(\text{multiples of 4}) \)** **Multiples of 4:** 4 \[ P(\text{multiples of 4}) = \frac{1}{6} \] 5. **\( P(2 \text{ or } 3) \)** **Favorable outcomes:** 2, 3 \[ P(2 \text{ or } 3) = \frac{2}{6} = \frac{1}{3} \] 6. **\( P(7) \)** Since a 6-sided die only has numbers up to 6, getting a 7 is impossible. \[ P(7) = 0 \] 7. **\( P(5) \)** **Favorable outcome:** 5 \[ P(5) = \frac{1}{6} \] 8. **\( P(2 \text{ or higher}) \)** **Outcomes 2 or higher:** 2, 3, 4, 5, 6 \[ P(2 \text{ or higher}) = \frac{5}{6} \] ### Summary of Probabilities - \( P(\text{even}) = \frac{1}{2} \) - \( P(\text{multiples of 2}) = \frac{1}{2} \) - \( P(\text{odd}) = \frac{1}{2} \) - \( P(\text{multiples of 4}) = \frac{1}{6} \) - \( P(2 \text{ or } 3) = \frac{1}{3} \) - \( P(7) = 0 \) - \( P(5) = \frac{1}{6} \) - \( P(2 \text{ or higher}) = \frac{5}{6} \)