To find the probability of rolling an odd number on the first roll of a six-sided die and rolling an even number on the second roll, we can break it down into two parts:
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Probability of rolling an odd number on the first roll:
- The odd numbers on a six-sided die are 1, 3, and 5.
- There are 3 odd numbers out of 6 total numbers.
- Therefore, the probability of rolling an odd number is \( \frac{3}{6} = \frac{1}{2} \).
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Probability of rolling an even number on the second roll:
- The even numbers on a six-sided die are 2, 4, and 6.
- There are also 3 even numbers out of 6 total numbers.
- Therefore, the probability of rolling an even number is \( \frac{3}{6} = \frac{1}{2} \).
To find the combined probability of both events occurring (rolling an odd number first and then rolling an even number), we multiply the individual probabilities:
\[ P(\text{odd first roll}) \times P(\text{even second roll}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
So, the final answer is:
\( \frac{1}{4} \).