Question

Two dice are rolled together. The probability of getting a doublet is:

• A. \(\frac{2}{36}\)
• B. \(\frac{1}{36}\)
• C. \(\frac{1}{6}\)
• D. \(\frac{5}{6}\)

Answer 1

The Correct Option is C

Step 1: Understanding the experiment
When two dice are rolled simultaneously, each die has 6 faces numbered from 1 to 6.
The total number of possible outcomes when both dice are rolled together is calculated by multiplying the number of outcomes from each die:
Total outcomes = 6 × 6 = 36

Step 2: Define a doublet
A doublet is a situation where both dice show the same number. That means the outcome must be of the form (1,1), (2,2), ..., (6,6).
Let’s list all possible doublets:
- (1,1)
- (2,2)
- (3,3)
- (4,4)
- (5,5)
- (6,6)
There are a total of 6 favorable outcomes where a doublet appears.

Step 3: Apply probability formula
The probability of an event is given by:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substitute the known values:
\[ \text{Probability of getting a doublet} = \frac{6}{36} = \frac{1}{6} \]

Final Answer: The probability of getting a doublet when two dice are rolled is 1/6.