Two dice are rolled simultaneously. What is the probability of
getting 3 on first die?

Answer

To solve the problem of finding the probability of getting a 3 on the first die when two dice are rolled simultaneously, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sample Space**:
When rolling two dice, each die has 6 faces. Therefore, the total number of possible outcomes when rolling two dice is:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]

2. **Define the Favorable Outcomes**:
We want to find the probability of getting a 3 on the first die. The outcomes where the first die shows a 3 can be listed as follows:
- (3, 1)
- (3, 2)
- (3, 3)
- (3, 4)
- (3, 5)
- (3, 6)

Thus, there are 6 favorable outcomes where the first die shows a 3.

3. **Calculate the Probability**:
The probability of an event is defined as the number of favorable outcomes divided by the total number of outcomes. Therefore, the probability \( P \) of getting a 3 on the first die is:
\[ P(\text{3 on first die}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{6}{36} \]

4. **Simplify the Probability**:
We can simplify \( \frac{6}{36} \):
\[ P(\text{3 on first die}) = \frac{1}{6} \]

### Final Answer:
The probability of getting a 3 on the first die is \( \frac{1}{6} \).

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