To find the probability of rolling an even number on the first roll and a number greater than 1 on the second roll with a single die, let's break down the problem:
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Determine the outcomes for each roll:
- A standard die has six faces showing the numbers 1, 2, 3, 4, 5, and 6.
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Calculate the probability of rolling an even number on the first roll:
- The even numbers on a die are 2, 4, and 6.
- There are 3 even numbers out of a total of 6 possible outcomes.
\[ P(\text{even on first roll}) = \frac{3}{6} = \frac{1}{2} \]
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Calculate the probability of rolling a number greater than 1 on the second roll:
- The numbers greater than 1 on a die are 2, 3, 4, 5, and 6.
- There are 5 numbers greater than 1 out of a total of 6 possible outcomes.
\[ P(\text{number > 1 on second roll}) = \frac{5}{6} \]
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Calculate the combined probability:
- Since the two rolls are independent events, the total probability can be found by multiplying the probabilities of each event.
\[ P(\text{even on first roll and number > 1 on second roll}) = P(\text{even on first roll}) \times P(\text{number > 1 on second roll}) = \frac{1}{2} \times \frac{5}{6} \]
\[ = \frac{5}{12} \]
Thus, the probability of rolling an even number the first time and a number greater than 1 the second time is
\[ \boxed{\frac{5}{12}}. \]