Math Problem Statement

If two 6-sided dice are rolled, what is the probability of rolling double 2s?

Solution

The problem asks for the probability of rolling double 2s when two 6-sided dice are rolled.

  1. Each die has 6 faces, with numbers from 1 to 6. The total number of outcomes when rolling two dice is: 6×6=366 \times 6 = 36

  2. Rolling double 2s means that both dice show a 2. There is exactly one outcome where this happens: (2, 2).

  3. The probability is the number of favorable outcomes (rolling double 2s) divided by the total number of possible outcomes: Probability=136\text{Probability} = \frac{1}{36}

So, the probability of rolling double 2s is 136\frac{1}{36}.

Would you like more details on how probability works or have any questions?

Here are 5 related questions:

  1. What is the probability of rolling double 6s?
  2. What is the probability of rolling two even numbers?
  3. How would the probability change if the dice had more sides?
  4. What is the probability of rolling at least one 2?
  5. How does this compare to the probability of rolling any double?

Tip: In dice problems, always count the total number of possible outcomes to determine probabilities!

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Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics

Formulas

Probability = favorable outcomes / total outcomes

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8