Three dice are thrown. What is the probability of getting a triplet?

Options

A. `(1)/(6)`
B. `(1)/(18)`
C. `(1)/(36)`
D. `(1)/(72)`

Explanation

To find the probability of getting a triplet when three dice are thrown, we can follow these steps:

### Step 1: Understand the concept of a triplet
A triplet means that all three dice show the same number. The possible outcomes for each die are 1, 2, 3, 4, 5, or 6. Therefore, the triplet outcomes can be (1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4), (5, 5, 5), and (6, 6, 6).

### Step 2: Count the number of favorable outcomes
Since there are 6 different numbers that can appear on the dice, the favorable outcomes for getting a triplet 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 total number of outcomes
When throwing three dice, each die has 6 faces. Therefore, the total number of outcomes when throwing three dice is calculated as:
\[ \text{Total outcomes} = 6 \times 6 \times 6 = 6^3 = 216 \]

### Step 4: Calculate the probability of getting a triplet
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:
\[ P(\text{Triplet}) = \frac{6}{216} = \frac{1}{36} \]

### Final Answer
The probability of getting a triplet when three dice are thrown is \( \frac{1}{36} \).

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