To find the probability of rolling an odd number on the first roll of a six-sided die and 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.
- So, there are 3 odd numbers out of 6 possible outcomes.
- The probability of rolling an odd number is: \[ P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \]
-
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 possible outcomes.
- 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 two rolls are independent events, we multiply the probabilities: \[ P(\text{odd on 1st and even on 2nd}) = P(\text{odd}) \times P(\text{even}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
Thus, the probability of rolling an odd number on the first roll and an even number on the second roll is:
\[ \frac{1}{4} \]
So the answer is:
\(\frac{1}{4}\).