To solve this probability problem, we need to analyze two parts: the probability of rolling an odd number on the first roll of a six-sided die and the probability of rolling an even number on the second roll.
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Calculating the 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 a total of 6 possible outcomes.
- Thus, the probability of rolling an odd number is: \[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \]
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Calculating the 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 a total of 6 possible outcomes.
- Thus, the probability of rolling an even number is: \[ P(\text{even}) = \frac{3}{6} = \frac{1}{2} \]
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Calculating the combined probability: Since the rolls are independent, we can multiply the probabilities of the two events: \[ P(\text{odd on first roll and even on second roll}) = P(\text{odd}) \times P(\text{even}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
Therefore, the probability of rolling an odd number on the first roll and an even number on the second roll is \(\frac{1}{4}\).
The correct answer is B) 1/4.