Math Problem Statement

We roll a fair dice three times.

Solution

When rolling a fair die three times, each roll has 6 possible outcomes (1 through 6), and the total number of possible outcomes is:

6×6×6=63=2166 \times 6 \times 6 = 6^3 = 216

This forms the basis for solving many probability-related questions involving three dice rolls.

Would you like to explore specific scenarios or calculations, such as:

  1. What is the probability of rolling a sum greater than a certain number?
  2. What is the probability of rolling three of the same number (triples)?
  3. What is the probability of getting at least one "6"?
  4. What is the expected value of the sum of the three rolls?
  5. How does the distribution of sums look?

Tip: When calculating probabilities for multiple dice rolls, always break down complex problems into smaller, manageable parts.

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Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics

Formulas

Total outcomes for multiple independent events: n^k
Basic probability formula: favorable outcomes / total outcomes

Theorems

Multiplication Principle of Counting

Suitable Grade Level

Grades 8-10