Question

Two dice are thrown at the same time. What is the probability that the difference of the numbers appearing on top is zero?

• A. \(\frac{1}{36}\)
• B. \(\frac{1}{6}\)
• C. \(\frac{5}{18}\)
• D. \(\frac{5}{36}\)

Hint:

When working with two dice, the total number of outcomes is always 36. Memorizing the number of outcomes for common events (like getting a specific sum, a doublet, etc.) can save time.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
We need to find the probability of a specific event when two dice are thrown. The total number of possible outcomes is the product of the number of faces on each die. The number of favorable outcomes is the count of outcomes that satisfy the given condition.

Step 2: Key Formula or Approach:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \] - Total outcomes when throwing two dice = \(6 \times 6 = 36\).
- We need to find the outcomes where the difference of the numbers is zero.

Step 3: Detailed Explanation:
The difference between the numbers on the two dice is zero only if the numbers are the same. These outcomes are called doublets.
The favorable outcomes are:
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
The number of favorable outcomes is 6.
The total number of possible outcomes is 36.
Now, calculate the probability:
\[ P(\text{difference is zero}) = \frac{6}{36} = \frac{1}{6} \]

Step 4: Final Answer:
The probability is \(\frac{1}{6}\).