How to Find the Probability of a Dice Sum

Step-by-step solution

1. Count the total outcomes.

   $$6 \times 6 = 36$$

   Why: Each die has six outcomes, and the two dice combine independently.

2. List the pairs that sum to 7.

   $$(1, 6),\ (2, 5),\ (3, 4),\ (4, 3),\ (5, 2),\ (6, 1)$$

   Why: Six ordered pairs give a sum of 7.

3. Divide and simplify.

   $$\frac{6}{36} = \frac{1}{6}$$

   Why: Probability is favourable outcomes over possible outcomes.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $\text{sum of } 2$

   Show answer

   $\frac{1}{36}$

2. 2

   $\text{sum of } 12$

   Show answer

   $\frac{1}{36}$

3. 3

   $\text{sum of } 5$

   Show answer

   $\frac{1}{9}$

4. 4

   $\text{sum of } 10$

   Show answer

   $\frac{1}{12}$

5. 5

   $\text{sum of } 3$

   Show answer

   $\frac{1}{18}$