what are the odds of either of two dice showing an even number?

To calculate the probability of either of two dice showing an even number, we follow these steps:

1. **Total outcomes:** Since each die has 6 faces, rolling two dice gives \(6 \times 6 = 36\) possible outcomes.

2. **Even numbers on a die:** The even numbers on a die are 2, 4, and 6. So, for any single die, the probability of showing an even number is:
   \[
   P(\text{even on one die}) = \frac{3}{6} = \frac{1}{2}
   \]

3. **Probability of both dice not showing an even number:** The probability that both dice show an odd number (i.e., no die shows an even number) is:
   \[
   P(\text{both odd}) = \frac{3}{6} \times \frac{3}{6} = \frac{9}{36}
   \]

4. **Probability of either die showing an even number:** The probability that at least one die shows an even number is the complement of both dice showing odd numbers. This is calculated as:
   \[
   P(\text{either even}) = 1 - P(\text{both odd}) = 1 - \frac{9}{36} = \frac{27}{36} = \frac{3}{4}
   \]

So, the probability that either of two dice shows an even number is \( \frac{3}{4} \) or 75%.

Would you like further clarification or more details?

Here are some related questions to deepen understanding:

1. What is the probability that both dice show even numbers?
2. What is the probability that neither die shows an even number?
3. What is the probability that exactly one die shows an even number?
4. How does the probability change if three dice are rolled instead of two?
5. What is the probability of rolling a sum that is an even number with two dice?

**Tip:** To find the complement probability, subtract the probability of the opposite event from 1.

What are the odds of either of two dice showing an even number?

Discover the probability of either of two dice showing an even number. This problem involves key concepts in probability such as the complement rule and basic combinatorics. Learn how to calculate the odds step-by-step, ideal for students in Grades 6-8.

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