Question

When rolling a 6-sided die twice, determine P(sum of 6).

twelve thirty sixths
seven thirty sixths
five thirty sixths
two sixths

Answer 1

To determine the probability of rolling a sum of 6 when rolling a 6-sided die twice, we can start by listing all the possible outcomes that result in a sum of 6. The pairs of die rolls that achieve this are:

1. (1, 5)
2. (2, 4)
3. (3, 3)
4. (4, 2)
5. (5, 1)

These combinations give us a total of 5 outcomes that result in a sum of 6.

Next, we need to determine the total number of possible outcomes when rolling a 6-sided die twice. Since each die has 6 faces, the total outcomes are:

\[
6 \times 6 = 36
\]

Now we can find the probability \( P \) of rolling a sum of 6 by dividing the number of favorable outcomes by the total number of outcomes:

\[
P(\text{sum of 6}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{5}{36}
\]

Thus, the answer is **five thirty sixths**, or \( \frac{5}{36} \).