In a single throw of two dice .Find the probability of doublet ?

Options

A. `(1)/(6)`
B. `(5)/(6)`
C. `(1)/(9)`
D. `(1)/(18)`

Answer

To find the probability of getting a doublet when throwing two dice, we can follow these steps:

### Step 1: Understand the total outcomes when throwing two dice.
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 for doublets.
A doublet occurs when both dice show the same number. The possible doublets are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)

Thus, there are a total of 6 favorable outcomes for doublets.

### Step 3: Calculate the probability of getting a doublet.
The probability \( P \) of an event is given by the formula:
\[ P(\text{Doublet}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} \]
Substituting the values we found:
\[ P(\text{Doublet}) = \frac{6}{36} \]

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

### Final Answer:
The probability of getting a doublet when throwing two dice is \( \frac{1}{6} \).

---