Certainly! Let's determine the probability that the sum of the scores on two dice, each numbered from 1 to 6, will be 4.
1. Determine Total Possible Outcomes:
When two dice are rolled, each die has 6 faces, which means each die can land on any one of 6 different numbers. Therefore, the total number of possible outcomes when two dice are rolled together is calculated as:
[tex]\[
6 \times 6 = 36
\][/tex]
So, there are 36 total possible outcomes.
2. Identify Favorable Outcomes:
Next, we need to identify all the possible outcomes where the sum of the scores on the two dice equals 4. These outcomes are:
- (1, 3): The first die shows 1 and the second die shows 3.
- (2, 2): The first die shows 2 and the second die shows 2.
- (3, 1): The first die shows 3 and the second die shows 1.
We can see that there are 3 favorable outcomes where the sum is 4.
3. Calculate the Probability:
Probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. Therefore, the probability that the sum of the scores on the two dice will be 4 is:
[tex]\[
\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{3}{36}
\][/tex]
4. Simplify the Fraction:
Simplifying the fraction \(\frac{3}{36}\):
[tex]\[
\frac{3}{36} = \frac{1}{12}
\][/tex]
5. Convert to Decimal (if needed):
The fraction \(\frac{1}{12}\) as a decimal is approximately:
[tex]\[
0.0833 \text{ (rounded to four decimal places)}
\][/tex]
Therefore, the probability that the sum of the scores on the two dice will be 4 is [tex]\(\frac{1}{12}\)[/tex] or approximately 0.0833.
