Two dice are rolled simultaneously . Find the probability of
Getting the sum as a prime number .

Options

A. `3/5`
B. `5/(12)`
C. `1/2`
D. `3/4`

Answer

To solve the problem of finding the probability of getting a sum that is a prime number when two dice are rolled, we can follow these steps:

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

### Step 2: Identify Prime Numbers
Next, we need to identify the prime numbers that can be obtained as sums when rolling two dice. The possible sums range from 2 (1+1) to 12 (6+6). The prime numbers within this range are:
- 2
- 3
- 5
- 7
- 11

### Step 3: Find Favorable Outcomes for Each Prime Sum
Now, we will find the combinations of dice rolls that result in each of these prime sums:

- **Sum = 2**: (1, 1) → 1 outcome
- **Sum = 3**: (1, 2), (2, 1) → 2 outcomes
- **Sum = 5**: (1, 4), (2, 3), (3, 2), (4, 1) → 4 outcomes
- **Sum = 7**: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) → 6 outcomes
- **Sum = 11**: (5, 6), (6, 5) → 2 outcomes

Now, we will add up all the favorable outcomes:
\[ \text{Total Favorable Outcomes} = 1 + 2 + 4 + 6 + 2 = 15 \]

### Step 4: Calculate the Probability
The probability \( P \) of getting a sum that is a prime number is given by the formula:
\[ P(\text{Prime Sum}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{15}{36} \]

### Step 5: Simplify the Probability
Now, we can simplify the fraction:
\[ \frac{15}{36} = \frac{5}{12} \]

### Final Answer
Thus, the probability of getting a sum that is a prime number when two dice are rolled is:
\[ \boxed{\frac{5}{12}} \]

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