To determine the probability of rolling a sum of 6 when rolling a 6-sided die twice, we need to follow these steps:
1. Identify the possible outcomes for each die roll:
Each die can land on any of the numbers between 1 and 6, so there are 6 possible outcomes for one die roll.
2. Find the total number of possible outcomes for two dice rolls:
For two dice rolls, the total number of possible outcomes is the product of the outcomes of the individual rolls:
[tex]\[
6 \times 6 = 36
\][/tex]
3. List all the combinations of two dice rolls that sum to 6:
The combinations that produce a sum of 6 are:
[tex]\[
(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
\][/tex]
There are 5 such combinations.
4. Calculate the theoretical probability:
The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. Here, the number of favorable outcomes is 5, and the total number of possible outcomes is 36:
[tex]\[
P(\text{sum of 6}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{5}{36}
\][/tex]
Thus, the theoretical probability [tex]\(P(\)[/tex]sum of 6[tex]\()\)[/tex] when rolling a 6-sided die twice is:
[tex]\[
\boxed{\frac{5}{36}}
\][/tex]
