A red die and a blue die are thrown. What is the probability that the numbers on the two dice are different?

When throwing two dice, each die has 6 faces, so there are \( 6 \times 6 = 36 \) possible outcomes when rolling two dice.

Now, to find the probability that the numbers on the red die and the blue die are different, we need to subtract the outcomes where the numbers on both dice are the same.

### Step-by-Step Breakdown:

1. **Total outcomes:** Since each die has 6 faces, there are 36 possible outcomes in total.

2. **Favorable outcomes (numbers are the same):** The numbers on both dice will be the same in the following cases:
   - (1, 1)
   - (2, 2)
   - (3, 3)
   - (4, 4)
   - (5, 5)
   - (6, 6)

   So, there are 6 outcomes where the numbers are the same.

3. **Outcomes where numbers are different:** There are \( 36 - 6 = 30 \) outcomes where the numbers are different.

4. **Probability:** The probability that the numbers are different is the ratio of favorable outcomes to total outcomes:
   \[
   P(\text{different numbers}) = \frac{30}{36} = \frac{5}{6}
   \]

Thus, the probability that the numbers on the two dice are different is \( \frac{5}{6} \).

Would you like more details, or do you have any questions?

Here are 5 related questions for further practice:

1. What is the probability that the numbers on the two dice are the same?
2. What is the probability of rolling a sum of 7 with two dice?
3. What is the probability of rolling an even number on both dice?
4. If one die is a red die and one is a blue die, what is the probability that the red die shows a higher number?
5. What is the probability of rolling a sum greater than 8?

**Tip:** Always ensure to count all possible outcomes to verify your probability calculations!

Learn how to calculate the probability that two dice show different numbers. This step-by-step explanation covers key probability concepts and breaks down how to find the number of favorable outcomes compared to total outcomes. Perfect for students in Grades 6-8.

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