Absolutely, let's solve this step-by-step.
First, let's determine the total number of possible outcomes when rolling two dice:
1. Calculating Total Number of Possible Outcomes:
- Each die has 6 faces.
- Therefore, the total number of possible outcomes when rolling two dice is:
[tex]\[
6 \times 6 = 36
\][/tex]
Now, let's identify the number of favorable outcomes where the sum of the numbers on the two dice equals 3:
2. Identifying Favorable Outcomes:
- We list all possible combinations of rolling two dice where the sum is 3:
- (1, 2)
- (2, 1)
- So, there are 2 favorable outcomes.
3. Calculating the Probability:
- The probability [tex]\( P \)[/tex] of an event happening is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
- Therefore, the probability [tex]\( P \)[/tex] that the sum of the numbers on two dice is 3 is:
[tex]\[
P(\text{sum is 3}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{2}{36}
\][/tex]
- Simplifying this fraction, we get:
[tex]\[
P(\text{sum is 3}) = \frac{1}{18}
\][/tex]
4. Expressing the Probability as a Decimal:
- To express this probability as a decimal, we divide:
[tex]\[
\frac{1}{18} \approx 0.05555555555555555
\][/tex]
- Rounding this to 4 decimal places:
[tex]\[
0.0556
\][/tex]
So, the probability [tex]\( P \)[/tex] that the sum of the numbers on two dice is 3, expressed as a decimal rounded to 4 places, is:
[tex]\[
P(\text{sum is 3}) \approx 0.0556
\][/tex]
Hence, the final result is:
- Total number of possible outcomes: 36
- Number of favorable outcomes: 2
- Probability that the sum is 3: [tex]\( \approx 0.0556 \)[/tex]
