A pair of balance die are rolled. What is the probability of not rolling the doubles

When a pair of balanced dice (or fair dice) are rolled, each die has 6 faces, so there are a total of \(6 \times 6 = 36\) possible outcomes.

### Rolling Doubles
Doubles occur when both dice show the same number. The possible doubles are:
- (1, 1)
- (2, 2)
- (3, 3)
- (4, 4)
- (5, 5)
- (6, 6)

There are 6 outcomes where doubles occur.

### Probability of Rolling Doubles
The probability of rolling doubles is:
\[
P(\text{Doubles}) = \frac{6}{36} = \frac{1}{6}
\]

### Probability of Not Rolling Doubles
The probability of not rolling doubles is the complement of the probability of rolling doubles:
\[
P(\text{Not Doubles}) = 1 - P(\text{Doubles}) = 1 - \frac{1}{6} = \frac{5}{6}
\]

So, the probability of not rolling doubles is \(\frac{5}{6}\).

Would you like more details on this or have any further questions?

Here are some related questions:
1. What is the probability of rolling a sum of 7 with two dice?
2. How many distinct sums can be rolled with two dice?
3. What is the probability of rolling at least one 6 with two dice?
4. If you roll two dice, what is the probability of rolling a sum greater than 8?
5. What is the expected value of the sum of the numbers when rolling two dice?
6. How does the probability of rolling doubles change with three dice?
7. What is the probability of rolling a sum of 9 with two dice?
8. What is the probability of rolling at least one double in three rolls of two dice?

**Tip:** Understanding the concept of complements in probability can simplify many calculations by allowing you to find the probability of an event not happening instead of directly calculating the event itself.

Discover the probability of not rolling doubles with a pair of balanced dice. Learn how to calculate probabilities using complements and understand basic concepts of probability theory. Suitable for Grades 6-8 students and anyone interested in probability calculations.

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