In a single throw of three dice, find the probability of getting the same number on all the three dice.

Options

A. `5/12`
B. `17/72`
C. `55/72`
D. None of these

Explanation

To find the probability of getting the same number on all three dice when thrown simultaneously, follow these steps:

### Step 1: Determine the total outcomes
When throwing three dice, each die has 6 faces. Therefore, the total number of outcomes when throwing three dice is calculated as:
\[ \text{Total Outcomes} = 6 \times 6 \times 6 = 216 \]

### Step 2: Identify the successful outcomes
The successful outcomes occur when all three dice show the same number. The possible outcomes for this scenario are:
- All dice show 1 (1, 1, 1)
- All dice show 2 (2, 2, 2)
- All dice show 3 (3, 3, 3)
- All dice show 4 (4, 4, 4)
- All dice show 5 (5, 5, 5)
- All dice show 6 (6, 6, 6)

Thus, there are 6 successful outcomes (one for each number from 1 to 6).

### Step 3: Calculate the probability
The probability \( P \) of getting the same number on all three dice is given by the ratio of successful outcomes to total outcomes:
\[ P = \frac{\text{Number of Successful Outcomes}}{\text{Total Outcomes}} = \frac{6}{216} \]

### Step 4: Simplify the probability
Now, simplify the fraction:
\[ P = \frac{6}{216} = \frac{1}{36} \]

### Final Answer
The probability of getting the same number on all three dice is:
\[ \boxed{\frac{1}{36}} \]

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