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When it comes to understanding probability, a great place to start is empirical probability. Unlike theoretical probability, which is based on predicting what should happen, empirical probability is observed and recorded from actual experiments or trials.
Empirical probability is calculated using the formula:

• Empirical Probability = \( \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}} \)

In the context of rolling dice, or any similar experiment, this means observing how often the event you're interested in occurs. If, for example, the sum of 7 occurs in 3 out of 10 trials, then the empirical probability would be \( \frac{3}{10} \), or 0.3.
The empirical probability provides a snapshot of what actually happens in practice, rather than what should happen in an ideal world. As you gather more data, the empirical probability can change, potentially converging to the theoretical probability in very large samples.

Dice are fascinating tools for probability problems because each side has an equal chance of landing face up. When rolling two six-sided dice, each one has one of 6 outcomes, making for a total of 36 possible combinations.
To focus on the "sum of dice," we consider the sum of both numbers shown by the dice when rolled. Common outcomes range from 2 (1+1) to 12 (6+6).
Some sums are more likely to occur than others due to the number of combinations that can produce them. Specifically, the sum of 7 can occur through these combinations:

• (1,6)
• (2,5)
• (3,4)
• (4,3)
• (5,2)
• (6,1)

There are 6 ways to make a sum of 7, which is why it’s among the most common outcomes. Sectioning it off visually can aid in recognizing such patterns and calculating probabilities.

When conducting experiments like rolling dice, it's essential to understand the concepts of trials and outcomes. Each throw of the dice is called a trial, and what you observe as a result of that throw is the outcome.
In a given experiment, the total number of trials represents how many times the experiment has been conducted. For example, if two dice are rolled 10 times, we have 10 trials.
Outcomes can vary, with some having specific interest due to their properties, such as the sum in dice rolls. Particularly for probability assessments like empirical probability, it’s crucial to recognize and categorize these outcomes to assess the frequency of certain results.
Keep in mind that increasing the number of trials generally gives a clearer picture of the actual probabilities involved. This is why large samples often produce more reliable probabilities. The beauty of trials and outcomes lies in their ability to model real-world uncertain events effectively.