Two dice are thrown at the same time. Find the probability of getting :
same number on both dice.

Answer

To find the probability of getting the same number on both dice when two dice are thrown, 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
Favorable outcomes are the cases where both dice show the same number. The possible outcomes for this scenario are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)

Thus, the total number of favorable outcomes is:
\[ \text{Favorable Outcomes} = 6 \]

### Step 3: Calculate the probability
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, the probability \( P \) of getting the same number on both dice is:
\[ P(\text{same number}) = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{6}{36} \]

### Step 4: Simplify the probability
Now, we simplify the fraction:
\[ P(\text{same number}) = \frac{6}{36} = \frac{1}{6} \]

### Final Answer
Thus, the probability of getting the same number on both dice is:
\[ \frac{1}{6} \]

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