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In probability, an event is an outcome or a set of outcomes from a random experiment. Think of it as something we are interested in observing. For instance, in the example given, Event A represents selecting an adult with blue eyes. It's one specific result among many possibilities when choosing a person randomly.

Complementary events are pairs of events that cover all possible outcomes of an experiment. If one happens, the other cannot, and vice versa. For instance, in the context of the problem, Event A is selecting an adult with blue eyes. The complementary event \(\bar{A}\) is selecting an adult without blue eyes.
If the probability of Event A is known, the probability of the complementary event \(\bar{A}\) can easily be found using the formula:
\[P(\bar{A}) = 1 - P(A)\]
Given this rule, complementary events always add up to 1.

Calculating probability is essentially measuring how likely an event is to occur. For an event A, the probability, written as \(P(A)\), tells you the chance of that event happening. It's calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
For example: If we had data indicating that 30 out of 100 randomly selected adults have blue eyes, the probability \(P(A)\) would be:
\[P(A) = \frac{30}{100} = 0.30\]
This means there's a 30% chance of picking a blue-eyed adult. Similarly, for the complementary event \(\bar{A}\) (not having blue eyes), the probability \[P(\bar{A}) = 1 - P(A) = 1 - 0.30 = 0.70\]
That indicates a 70% chance of selecting an adult without blue eyes.