A die is thrown twice , what is the probability of getting a sum 7 from both the throws ?

Options

A. `(5)/(18)`
B. `(1)/(18)`
C. `(1)/(9)`
D. `(1)/(6)`

Explanation

To solve the problem of finding the probability of getting a sum of 7 when a die is thrown twice, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Total Outcomes**:
When a die is thrown, it has 6 faces. When thrown twice, the total number of outcomes can be calculated as:
\[ \text{Total Outcomes} = 6 \times 6 = 36 \]

2. **Identify Favorable Outcomes for Sum of 7**:
We need to find the combinations of the two throws that result in a sum of 7. The possible pairs (first throw, second throw) that give a sum of 7 are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)

Counting these combinations, we find there are 6 favorable outcomes.

3. **Calculate the Probability**:
The probability of an event is given by the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{6}{36} = \frac{1}{6} \]

### Final Answer:
The probability of getting a sum of 7 from both throws of the die is \(\frac{1}{6}\).

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