In a single throw of three dice, the probability of getting the same number on the three dice is

Options

A. `1/6`
B. `1/36`
C. `5/216`
D. `7/216`

Answer

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

### Step 1: Determine the Total Number of Outcomes
When throwing three dice, each die has 6 faces. Therefore, the total number of possible outcomes when throwing three dice is calculated as follows:

\[ \text{Total Outcomes} = 6 \times 6 \times 6 = 216 \]

### Step 2: Determine the Favorable Outcomes
Next, we need to find the number of favorable outcomes where all three dice show the same number. The possible outcomes where the three dice show the same number are:

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

Thus, there are a total of 6 favorable outcomes.

### Step 3: Calculate the Probability
The probability \( P \) of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. Therefore, we can calculate the probability of getting the same number on all three dice as follows:

\[ P(\text{same number on 3 dice}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{6}{216} \]

### Step 4: Simplify the Probability
Now we simplify the fraction:

\[ \frac{6}{216} = \frac{1}{36} \]

### Conclusion
Thus, the probability of getting the same number on all three dice is:

\[ \frac{1}{36} \]

### Final Answer
The answer is option (b) \( \frac{1}{36} \).

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