To solve this problem, we need to determine the probability that the sum of the numbers on two 6-sided dice will be 3. Let's break this down step-by-step.
1. Total Possible Outcomes:
Since each die has 6 faces, when two dice are rolled, each die has 6 possible outcomes. Therefore, the total number of possible outcomes when rolling two dice is:
[tex]\[
6 \times 6 = 36
\][/tex]
2. Favorable Outcomes:
We need to identify all the pairs of numbers on the two dice that add up to 3.
Considering the combinations:
- Die 1 shows 1 and Die 2 shows 2 (1+2=3)
- Die 1 shows 2 and Die 2 shows 1 (2+1=3)
These are the only two outcomes where the sum is 3. Hence, there are 2 favorable outcomes.
3. Probability Calculation:
The probability of an event 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 the two dice is 3 is:
[tex]\[
P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{2}{36} = \frac{1}{18}
\][/tex]
Therefore, the probability that the sum of the numbers on the two dice will be 3 is:
[tex]\[
\boxed{\frac{1}{18}}
\][/tex]
