Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is

Options

A. `(5)/(18)`
B. `(7)/(36)`
C. `(7)/(18)`
D. `(5)/(36)`

Answer

To solve the problem of finding the probability of getting the sum of 2, 8, or 12 when two dice are thrown, we can follow these steps:

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

### Step 2: Find the Favorable Outcomes for Each Sum
Now, we need to find the number of favorable outcomes for each of the sums: 2, 8, and 12.

- **Sum = 2**: The only combination that gives a sum of 2 is (1, 1).
- **Favorable outcomes for sum 2**: 1

- **Sum = 8**: The combinations that give a sum of 8 are:
- (2, 6)
- (3, 5)
- (4, 4)
- (5, 3)
- (6, 2)
- **Favorable outcomes for sum 8**: 5

- **Sum = 12**: The only combination that gives a sum of 12 is (6, 6).
- **Favorable outcomes for sum 12**: 1

### Step 3: Calculate the Total Favorable Outcomes
Now, we can sum the favorable outcomes for all the required sums:
\[ \text{Total Favorable Outcomes} = \text{Favorable for 2} + \text{Favorable for 8} + \text{Favorable for 12} = 1 + 5 + 1 = 7 \]

### Step 4: Calculate the Probability
The probability of getting a sum of 2, 8, or 12 is given by the ratio of the total favorable outcomes to the total outcomes:
\[ \text{Probability} = \frac{\text{Total Favorable Outcomes}}{\text{Total Outcomes}} = \frac{7}{36} \]

### Final Answer
Thus, the probability of getting the sum of 2 or 8 or 12 when two dice are thrown is:
\[ \frac{7}{36} \]

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