A single die is rolled twice. Find the probability of rolling an odd number the first time and a number greater than 2 the second time. Find the probability of rolling an odd number the first time and a number greater than 2 the second time. \( \square \) (Type an integer or a simplified fraction.)

To solve the problem, we first identify the outcomes for each roll of the die. There are 6 faces on a die: 1, 2, 3, 4, 5, and 6. 1. **Probability of rolling an odd number (1, 3, or 5)**: There are 3 odd numbers out of 6 possible outcomes. \[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \] 2. **Probability of rolling a number greater than 2 (3, 4, 5, or 6)**: There are 4 numbers greater than 2 out of 6 possible outcomes. \[ P(>2) = \frac{4}{6} = \frac{2}{3} \] 3. **Combined probability**: Since the rolls are independent, we multiply the probabilities: \[ P(\text{odd first and >2 second}) = P(\text{odd}) \times P(>2) = \frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3} \] Thus, the probability of rolling an odd number the first time and a number greater than 2 the second time is \(\frac{1}{3}\).