1. The problem is to find the complement of an event $q$ in probability or set theory. 2. The complement of an event $q$, denoted as $q^c$ or $\overline{q}$, consists of all outcomes not in $q$. 3. The formula for the complement is: $$P(q^c) = 1 - P(q)$$ This means the probability of the complement is one minus the probability of the event. 4. Important rules: - The event and its complement are mutually exclusive. - Their probabilities add up to 1. 5. Example: If $P(q) = 0.3$, then $$P(q^c) = 1 - 0.3 = 0.7$$ 6. This means the complement event has a probability of 0.7, representing all outcomes where $q$ does not occur. This explanation applies to probability and set theory contexts.