Question

Madeline rolls two six-sided dice. The probability of getting a specific number on either of the six-sided dice is independent.
What is the probability of rolling a four and a five? Round your answer to four decimal places.

Answer 1

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.

1. **Total Outcomes**: Each die has 6 sides, so when rolling two dice, the total number of outcomes is:
\[
6 \times 6 = 36
\]

2. **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).

3. **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:
\[
P = \frac{\text{Number of successful outcomes}}{\text{Total outcomes}} = \frac{2}{36} = \frac{1}{18}
\]

4. **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 \( \boxed{0.0556} \).