Sure, let's work through this step-by-step.
1. Determine the total number of outcomes when two dice are rolled:
- Each die has 6 faces numbered from 1 to 6.
- When rolling two dice, the total number of possible outcomes is the product of the number of faces on each die.
[tex]\[
\text{Total outcomes} = 6 \times 6 = 36
\][/tex]
So, there are 36 possible outcomes when rolling two dice.
2. Identify the favorable outcomes where the sum is 12:
- To get a sum of 12, both dice need to show a 6 since [tex]\(6 + 6 = 12\)[/tex].
- There is exactly one combination (6, 6) that adds up to 12.
[tex]\[
\text{Favorable outcomes} = 1
\][/tex]
3. Calculate the probability:
- Probability is defined as the number of favorable outcomes divided by the total number of possible outcomes.
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{36}
\][/tex]
4. Express the probability as a decimal and round to 4 decimal places:
- Converting the fraction [tex]\(\frac{1}{36}\)[/tex] to a decimal:
[tex]\[
\frac{1}{36} \approx 0.027777\ldots
\][/tex]
- Rounding to 4 decimal places, we get:
[tex]\[
\text{Probability} \approx 0.0278
\][/tex]
In summary, the total number of outcomes when two dice are rolled is 36. There is only 1 favorable outcome where the sum of the two dice is 12. The probability of rolling two dice and getting a sum of 12 is 0.0278 when rounded to 4 decimal places.
