To find the probability of rolling a four and a five with two six-sided dice, we need to consider the total outcomes and the successful outcomes.
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Total Outcomes: Each die has 6 sides, so when rolling two dice, the total number of outcomes is: \[ 6 \times 6 = 36 \]
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Successful Outcomes: We need to determine how many ways we can roll a four and a five. There are two scenarios for this:
- The first die shows a four and the second die shows a five.
- The first die shows a five and the second die shows a four.
Thus, there are 2 successful outcomes (4, 5) and (5, 4).
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Calculating Probability: The probability \( P \) of rolling a four and a five is given by the ratio of the number of successful outcomes to the total outcomes: \[ P = \frac{\text{Number of successful outcomes}}{\text{Total outcomes}} = \frac{2}{36} = \frac{1}{18} \]
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Rounding to Four Decimal Places: Now, we can convert \( \frac{1}{18} \) to a decimal: \[ \frac{1}{18} \approx 0.055555555... \] When rounded to four decimal places, this gives us: \[ 0.0556 \]
Thus, the probability of rolling a four and a five is \( \boxed{0.0556} \).