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

Answer

To find the probability of getting an even number on the first die when two dice are rolled simultaneously, we can follow these steps:

### Step 1: Determine the total number of outcomes
When two dice are rolled, each die has 6 faces. Therefore, the total number of outcomes when rolling two dice is calculated as:
\[ \text{Total outcomes} = 6 \times 6 = 36 \]

### Step 2: Identify the favorable outcomes for the first die being even
The even numbers on a die are 2, 4, and 6. We need to find all the outcomes where the first die shows an even number.

- If the first die is **2**, the possible outcomes are:
- (2,1), (2,2), (2,3), (2,4), (2,5), (2,6) → 6 outcomes

- If the first die is **4**, the possible outcomes are:
- (4,1), (4,2), (4,3), (4,4), (4,5), (4,6) → 6 outcomes

- If the first die is **6**, the possible outcomes are:
- (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) → 6 outcomes

Adding these favorable outcomes together:
\[ \text{Favorable outcomes} = 6 + 6 + 6 = 18 \]

### Step 3: Calculate the probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{18}{36} = \frac{1}{2} \]

### Conclusion
The probability of getting an even number on the first die when two dice are rolled is:
\[ \frac{1}{2} \]

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