The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

Options

A. 0
B. `(1)/(3)`
C. `(1)/(12)`
D. `(1)/(36)`

Answer

To solve the problem of finding the probability of obtaining an even prime number on each die when a pair of dice is rolled, we can follow these steps:

### Step 1: Understand the Problem
We need to find the probability of rolling two dice and getting an even prime number on each die.

### Step 2: Identify the Total Outcomes
When rolling two dice, each die has 6 faces. Therefore, the total number of outcomes when rolling two dice is:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]

### Step 3: Identify the Even Prime Numbers
The only even prime number is 2.

### Step 4: Determine Favorable Outcomes
For both dice to show an even prime number, both must show the number 2. Thus, the only favorable outcome is (2, 2).

### Step 5: Calculate the Probability
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Here, we have:
- Number of Favorable Outcomes = 1 (which is (2, 2))
- Total Outcomes = 36

So the probability is:
\[ \text{Probability} = \frac{1}{36} \]

### Conclusion
The probability of obtaining an even prime number on each die when a pair of dice is rolled is \(\frac{1}{36}\).

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