Question

What is the probability of rolling a 5 and a 6 with two six-sided dice?

Answer 1

To find the probability of rolling a 5 and a 6 with two six-sided dice, we first determine the total number of possible outcomes when rolling two dice. Each die has 6 faces, so when rolling two dice, the total number of outcomes is:

\[
6 \times 6 = 36
\]

Next, we identify the specific outcomes that satisfy our condition of rolling a 5 and a 6. There are two scenarios that meet this condition:

1. The first die shows a 5 and the second die shows a 6: (5, 6)
2. The first die shows a 6 and the second die shows a 5: (6, 5)

Thus, there are 2 favorable outcomes: (5, 6) and (6, 5).

Now we can calculate the probability:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{2}{36}
\]

This fraction simplifies to:

\[
\frac{1}{18}
\]

Therefore, the probability of rolling a 5 and a 6 with two six-sided dice is \(\frac{1}{18}\).