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When you roll two dice, each die can land on a number from 1 to 6. This means there is a wide range of combinations that can appear as outcomes. Each die acts independently, so the outcome on one die does not affect the other.
Given two dice, which we can label as Die A and Die B, each die when rolled has possibilities like:

• Die A: 1, 2, 3, 4, 5, or 6
• Die B: 1, 2, 3, 4, 5, or 6

The total number of outcomes when rolling two dice is calculated by multiplying the outcomes for Die A and Die B, so 6 outcomes from Die A times 6 outcomes from Die B result in 36 total possible outcomes.
This means that with two dice, you have 36 possible pairs of results that can appear on the top faces.

Probability is about finding how likely an event is to happen. To calculate probability, we need two key pieces of information:

• The number of desired or successful outcomes
• The total number of possible outcomes

For rolling doubles with two dice, successful outcomes are when both dice show the same number. As identified earlier, these are: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6). This gives us 6 successful outcomes.
The probability formula therefore can be set up as:\[ \text{Probability of rolling a double} = \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}} \]Inserting our numbers into the formula gives:\(\frac{6}{36}\).
This formula helps us recognize and calculate how frequent rolling doubles can be expected from two dice.

Fractions often need to be simplified to make them easier to understand or compare. Simplification involves reducing the numerator (top number) and the denominator (bottom number) to their smallest possible whole numbers.
In the fraction \(\frac{6}{36}\), both the numerator and denominator can be divided by their greatest common divisor (GCD). The GCD here is 6, which is the largest number that evenly divides both 6 and 36.
So, we divide the numerator and the denominator by 6:\[ \frac{6 \div 6}{36 \div 6} = \frac{1}{6} \]
By simplifying \(\frac{6}{36}\) to \(\frac{1}{6}\), we can easily understand that the probability of rolling the same number on both dice (a double) is 1 in 6 tries.