Final Answer:
Given p(e) = 0.23, the probability p(ec) can be calculated using the complement rule, where p(ec) = 1 - p(e) = 1 - 0.23 = 0.77.
Step-by-step explanation:
In probability theory, the complement rule states that the probability of an event not occurring (denoted as ec, the complement of event e) is equal to 1 minus the probability of the event occurring (p(e)). Therefore, if the probability of event e, denoted as p(e), is given as 0.23, then the probability of the event not occurring, p(ec), can be calculated as 1 minus the probability of event e. Mathematically, p(ec) = 1 - p(e). Substituting the given value, p(e) = 0.23, into the formula, p(ec) = 1 - 0.23 = 0.77.
In this context, p(ec) represents the probability of the complement of event e occurring. It could refer to the probability of an alternative outcome or the event not happening when event e occurs. Understanding the complement rule is essential in probability calculations, especially when dealing with scenarios where the direct probability of an event is known, enabling the determination of the probability of its complement.
Therefore, given the probability of event e as 0.23, the probability of its complement, p(ec), is found to be 0.77 using the complement rule, which helps in analyzing the likelihood of events and their non-occurrence in various probability scenarios.