Two fair dice are rolled together. The probability that the difference of numbers appearing is 1 will be

Options

A. `5/6`
B. `7/36`
C. `5/18`
D. `7/14`

Answer

To solve the problem of finding the probability that the difference of numbers appearing when two fair dice are rolled is 1, we can follow these steps:

### Step 1: Determine the total number of 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 favorable outcomes
Next, we need to find the outcomes where the difference between the numbers on the two dice is 1. The possible pairs (A, B) where |A - B| = 1 are:

- (1, 2)
- (2, 1)
- (2, 3)
- (3, 2)
- (3, 4)
- (4, 3)
- (4, 5)
- (5, 4)
- (5, 6)
- (6, 5)

Counting these pairs, we find there are 10 favorable outcomes.

### Step 3: Calculate the probability
The probability of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ P(\text{difference of 1}) = \frac{10}{36} = \frac{5}{18} \]

### Final Answer
Thus, the probability that the difference of numbers appearing is 1 when two fair dice are rolled is:
\[ \frac{5}{18} \]

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