Find the probability of getting the same number of two dice in a single throw of two dice.

Explanation

To find the probability of getting the same number on two dice in a single throw, we can follow these steps:

### Step 1: Determine the total outcomes when throwing two dice.
When throwing two dice, each die has 6 faces (numbered from 1 to 6). Therefore, the total number of outcomes (denoted as \( n_s \)) when throwing two dice can be calculated as:
\[ n_s = 6 \times 6 = 36 \]

### Step 2: Identify the favorable outcomes where both dice show the same number.
The favorable outcomes (denoted as \( n_f \)) for the event where both dice show the same number are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)

Thus, the number of favorable outcomes is:
\[ n_f = 6 \]

### Step 3: Calculate the probability.
The probability \( P \) of both dice showing the same number is given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[ P = \frac{n_f}{n_s} = \frac{6}{36} = \frac{1}{6} \]

### Final Answer:
The probability of getting the same number on two dice in a single throw is:
\[ \frac{1}{6} \]

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