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In any probability problem, such as determining the likeliness of having at least one boy in a family of three children, the term 'favorable outcomes' refers to the set of all possible events that satisfy the condition we're interested in. To visualize this, imagine each child as an independent event with two outcomes, either Boy (B) or Girl (G). Focussing on our condition, any combination that includes at least one 'B' represents a favorable outcome. This leads us to enumerate all combinations: BBB, BBG, BGB, BGG, GBB, GBG, and GGB.
Each of these combinations has at least one boy, making them favorable. The only combination left out is GGG, as it doesn't meet our requirement. When calculating probabilities, it is crucial to accurately identify and count these favorable outcomes correctly, as they form the basis for our calculations.

The 'total number of outcomes' is just as it sounds—every single possible event that could arise from a probabilistic scenario. In the context of our three-child family, we must consider all the gender combinations that could occur. For each child, there are 2 possibilities: Boy or Girl. Since there are three children, we raise the number of possibilities for one child to the power of three, i.e., using the formula \(2^n\), where \(n\) is the number of children, giving us \(2^3 = 8\) total outcomes.

We then list these possibilities to confirm that we have accounted for every potential outcome: BBB, BBG, BGB, BGG, GBB, GBG, GGB, and GGG. Understanding and determining the total number of outcomes is pivotal because it forms the denominator in our probability calculations and allows us to understand the probability in relation to the whole event space.

Probability formulas are used to translate our count of outcomes into a quantitative likelihood of an event occurring. The most fundamental formula for probability is quite straightforward: \[ Probability = \frac{Number \ of \ Favorable \ Outcomes}{Total \ Number \ of \ Outcomes} \]
Looking back at our example, we have 7 favorable outcomes and a total of 8 outcomes. Applying the formula, the probability for at least one boy in a three-child family is \(\frac{7}{8}\). Remember that the probabilities always range from 0 (an impossible event) to 1 (a certain event).

This formula can be adjusted or expanded depending on different types of probability problems, such as when dealing with dependent or independent events, conditional probabilities, or more complex scenarios like permutations and combinations in probability theory. However, the essence remains the same; we are comparing the number of ways an event we are tracking can occur against the backdrop of all possible events.