komplementreglen

The complement rule is a fundamental concept in probability theory. It states that the probability of an event not occurring is equal to one minus the probability of the event occurring. Mathematically, if P(A) represents the probability of event A occurring, then the probability of event A not occurring, denoted as P(A'), is given by P(A') = 1 - P(A). This rule is particularly useful when it is easier to calculate the probability of an event happening than the probability of it not happening, or vice versa. For example, if you are calculating the probability of getting at least one head when flipping a coin three times, it is often simpler to calculate the probability of getting no heads (all tails) and then subtract that from one. The complement rule applies to any event and its complement, where the complement of an event encompasses all possible outcomes that are not included in the event itself. Together, an event and its complement partition the entire sample space of possible outcomes, meaning that one of them must occur. This principle is a direct consequence of the axioms of probability, specifically the axiom that the probability of the sample space is 1.