Two dice are thrown. The probability that the sum of the points on two dice will be 7 is

Options

A. `(5)/(36)`
B. `(6)/(36)`
C. `(7)/(36)`
D. `(8)/(36)`

Answer

To find the probability that the sum of the points on two dice will be 7, we can follow these steps:

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

### Step 2: Identify the favorable outcomes for the sum of 7
Next, we need to find the combinations of the two dice that add up to 7. The pairs that give a sum of 7 are:
- (1, 6)
- (2, 5)
- (3, 4)
- (4, 3)
- (5, 2)
- (6, 1)

Counting these pairs, we find that there are 6 favorable outcomes.

### Step 3: Calculate the probability
The probability \( P \) of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} \]
Substituting the values we found:
\[ P(\text{Sum of 7}) = \frac{6}{36} \]

### Step 4: Simplify the probability
We can simplify \( \frac{6}{36} \):
\[ P(\text{Sum of 7}) = \frac{1}{6} \]

### Final Answer
Thus, the probability that the sum of the points on two dice will be 7 is:
\[ \frac{1}{6} \]

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