A game involves rolling two dice. You win if you roll a sum of 3 or doubles. What is the probability that you will win. Write your answer as a fraction in lowest terms. (ex. 1/6)

To determine the probability of winning the game, we need to analyze the outcomes when rolling two dice. We'll list all the outcomes and identify the winning ones, then calculate the probability.

### Step-by-Step Solution:

1. **Total Possible Outcomes:**
   - Each die has 6 faces.
   - Therefore, the total number of outcomes when rolling two dice is \(6 \times 6 = 36\).

2. **Winning Outcomes:**
   - You win if you roll a sum of 3 or if you roll doubles.

   **Sum of 3:**
   - The pairs that give a sum of 3 are:
     1. (1, 2)
     2. (2, 1)
   - Thus, there are 2 outcomes where the sum is 3.

   **Doubles:**
   - The pairs that are doubles are:
     1. (1, 1)
     2. (2, 2)
     3. (3, 3)
     4. (4, 4)
     5. (5, 5)
     6. (6, 6)
   - Thus, there are 6 outcomes where the dice show doubles.

   **Total Winning Outcomes:**
   - We need to combine the outcomes of rolling a sum of 3 and rolling doubles. Importantly, there are no overlaps between these two sets of outcomes.
   - Therefore, the total number of winning outcomes is \(2 + 6 = 8\).

3. **Calculating the Probability:**
   - The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
   \[
   \text{Probability of winning} = \frac{\text{Number of winning outcomes}}{\text{Total number of possible outcomes}} = \frac{8}{36}
   \]

4. **Simplify the Fraction:**
   - Simplify \(\frac{8}{36}\) by dividing the numerator and the denominator by their greatest common divisor, which is 4.
   \[
   \frac{8 \div 4}{36 \div 4} = \frac{2}{9}
   \]

### Conclusion:
The probability of winning the game by rolling a sum of 3 or doubles is \(\frac{2}{9}\).

Would you like more details or have any questions?

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Here are five questions you might ask:

1. How do you determine the number of total possible outcomes when rolling two dice?
2. Can you explain why there are no overlaps between the outcomes for a sum of 3 and doubles?
3. What is the method to simplify a fraction to its lowest terms?
4. How can the concept of probability be applied to real-life situations?
5. What is the importance of understanding probabilities in games of chance?

**Tip:** When calculating probabilities, always ensure to count each possible outcome correctly and simplify the resulting fraction to its lowest terms for clarity.

Discover the probability of winning a game involving two dice by rolling a sum of 3 or doubles. Detailed step-by-step solution provided, including calculations and simplification of fractions. Suitable for students in Grades 6-8.

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