A traditional number cube (or die) has 6 faces, numbered from 1 to 6. The even numbers on the cube are 2, 4, and 6, while the odd numbers are 1, 3, and 5.
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Calculating the probability of rolling an even number on the first roll:
- There are 3 even numbers (2, 4, 6) out of 6 total numbers.
- So, \( P(\text{even}) = \frac{3}{6} = \frac{1}{2} \).
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Calculating the probability of rolling an odd number on the second roll:
- There are 3 odd numbers (1, 3, 5) out of 6 total numbers.
- So, \( P(\text{odd}) = \frac{3}{6} = \frac{1}{2} \).
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Finding the overall probability:
- Since the rolls are independent events, we can multiply the probabilities: \[ P(\text{even on first roll and odd on second roll}) = P(\text{even}) \times P(\text{odd}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}. \]
Thus, the probability that the first roll lands on an even number and the second roll lands on an odd number is \(\frac{1}{4}\).