Math Problem Statement

What is the probability of rolling the same number on both dice? Give your answer as a fraction.

Solution

The question asks for the probability of rolling the same number on both dice, using the provided grid of all possible outcomes.

Step-by-Step Solution:

  1. Count Total Possible Outcomes:
    The grid shows 6×6=366 \times 6 = 36 total possible outcomes (since each die has 6 sides).

  2. Count Favorable Outcomes:
    Rolling the same number on both dice corresponds to the diagonal entries where (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)(1,1), (2,2), (3,3), (4,4), (5,5), (6,6).
    There are 6 favorable outcomes.

  3. Calculate the Probability:
    Probability =Number of Favorable OutcomesTotal Outcomes= \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}}.
    Thus, 636=16\frac{6}{36} = \frac{1}{6}.

Final Answer:

The probability of rolling the same number on both dice is 16\frac{1}{6}.

Let me know if you'd like a more detailed explanation!


Related Questions:

  1. What is the probability of rolling a sum of 7 with two dice?
  2. How many outcomes result in a sum less than 5?
  3. What is the probability of rolling at least one "1" with two dice?
  4. How many outcomes result in a product of the two dice being 12?
  5. What is the probability of rolling two numbers such that their difference is 2?

Tip:

To solve probability problems with dice, identify favorable outcomes visually from the grid to simplify calculations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics

Formulas

Probability = Number of Favorable Outcomes / Total Number of Outcomes

Theorems

Basic Probability Rules

Suitable Grade Level

Grades 5-7