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 problem:
We are rolling two dice together, and we need to find the probability of getting a doublet. A doublet is defined as a pair of dice showing the same number on both dice.

Step 2: Total number of possible outcomes:
Each die has 6 faces, so when two dice are rolled, the total number of possible outcomes is the product of the number of faces on each die:
\[ 6 \times 6 = 36 \] Thus, there are 36 possible outcomes when two dice are rolled.

Step 3: Number of favorable outcomes:
A doublet occurs when both dice show the same number. The possible doublets are:
\[ (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) \] So, there are 6 favorable outcomes for getting a doublet.

Step 4: Calculating the probability:
The probability of an event is given by the ratio of favorable outcomes to the total number of possible outcomes. Therefore, the probability of getting a doublet is:
\[ \text{Probability of doublet} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6} \]

Step 5: Conclusion:
The probability of getting a doublet when two dice are rolled is \( \frac{1}{6} \).