Math Problem Statement

Refer to the table below. Of the 36 possible outcomes, determine the number for which the sum (for both dice) is 7.

Solution

To determine the number of ways to roll a sum of 7 with two dice, we need to identify the pairs in the table where the sum of the two dice equals 7.

The possible sums of 7 are:

  • (1,6)
  • (2,5)
  • (3,4)
  • (4,3)
  • (5,2)
  • (6,1)

So, there are 6 ways to roll a sum of 7.

Would you like any further details or explanations on this? Here are 5 related questions for deeper understanding:

  1. How many total possible outcomes are there when rolling two dice?
  2. What is the probability of rolling a sum of 7 with two dice?
  3. Can other sums be rolled in the same number of ways as 7?
  4. How would the result change if the dice were weighted?
  5. How do different sums distribute over the possible outcomes in dice rolls?

Tip: The sum of 7 is the most frequent outcome when rolling two dice because there are more combinations that result in this sum than any other.

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Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics

Formulas

Sum of two numbers from dice

Theorems

Basic combinatorics in dice outcomes

Suitable Grade Level

Grades 6-8