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Probability theory is the branch of mathematics that deals with calculating the likelihood of different outcomes. It forms the basis for statistics and is essential for making predictions in various fields, from gambling to weather forecasting. At its core, probability theory tells us how to find the chance that something will happen.

When we calculate probability, we look at the ratio of the number of ways an event can occur to the number of all possible outcomes. This is expressed as a value between 0 and 1, where 0 means the event cannot happen and 1 means it certainly will happen. In the context of our dice problem, probability theory allows us to determine the likelihood of rolling certain sums with two dice.

Favorable outcomes are the specific results of an experiment or event that we are interested in and count towards the success of the event occurring. In terms of rolling dice, if we want to know the probability of rolling a sum of 6 or 7, our favorable outcomes would be any dice combinations that add up to these sums.

It's crucial when identifying favorable outcomes to consider all the combinations that satisfy our criteria. For instance, in the dice example, a sum of 6 could come from several different dice rolls like (1,5) or (3,3). These are simple enumerations where each unique pair is counted once as a favorable outcome. Calculating these correctly helps us to find the probability accurately.

The concept of possible outcomes revolves around the total number of distinct events that can result from a random experiment, regardless of whether they meet our success criteria. For two dice, each die can land on one of six faces, so the number of possible outcomes is found by considering all the combinations these two dice can take on.

To visualize this, you might imagine a grid with one die represented on the horizontal axis and the other on the vertical. This grid would have 36 positions, representing the pairs (1,1), (1,2), up to (6,6). Understanding the total possible outcomes is a key component, as it sets the denominator in our probability fraction and provides context to the number of favorable outcomes.