On rolling two dice at once, what is the probability of getting a sum of doublet less than 5 ?

Options

A. `(1)/(6)`
B. `(2)/(9)`
C. `(1)/(18)`
D. `(3)/(7)`

Answer

To solve the problem of finding the probability of getting a sum of doublets less than 5 when rolling two dice, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Sample Space**:
When rolling two dice, the total possible outcomes (sample space) is 6 (from the first die) × 6 (from the second die) = 36 outcomes.

2. **Identify Doublets**:
A doublet occurs when both dice show the same number. The possible doublets when rolling two dice are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)

Thus, there are a total of 6 doublets.

3. **Calculate the Sums of Doublets**:
Now, we need to find the sums of these doublets:
- (1, 1) → Sum = 2
- (2, 2) → Sum = 4
- (3, 3) → Sum = 6
- (4, 4) → Sum = 8
- (5, 5) → Sum = 10
- (6, 6) → Sum = 12

4. **Identify Doublets with Sums Less than 5**:
We need to find which of these doublets have a sum less than 5. The doublets that meet this criterion are:
- (1, 1) → Sum = 2
- (2, 2) → Sum = 4

Therefore, there are 2 doublets with sums less than 5.

5. **Calculate the Probability**:
The probability of an event is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Here, the number of favorable outcomes (doublets with sums less than 5) is 2, and the total number of outcomes is 36.

Thus, the probability is:
\[ P(\text{sum of doublets} < 5) = \frac{2}{36} = \frac{1}{18} \]

### Final Answer:
The probability of getting a sum of doublets less than 5 when rolling two dice is \( \frac{1}{18} \).