1. **Problem statement:** Formulate the complementary events (Gegenereignisse) for the following events when randomly marking answers to five tasks. 2. **Recall:** The complementary event of an event $A$ is the event that $A$ does not occur, denoted as $A^c$. 3. **Event c1:** "Exactly one answer is correct." - Complement: "Not exactly one answer is correct," which means either zero answers are correct or more than one answer is correct. - Formally: $c1^c = \{0 \text{ correct} \} \cup \{\geq 2 \text{ correct} \}$. 4. **Event c2:** "At least two answers are correct." - Complement: "Fewer than two answers are correct," i.e., zero or one answer is correct. - Formally: $c2^c = \{0 \text{ correct} \} \cup \{1 \text{ correct} \}$. 5. **Event c3:** "At most one task is wrong." - Since there are 5 tasks, "at most one task is wrong" means either zero or one task is wrong. - Complement: "More than one task is wrong," i.e., at least two tasks are wrong. - Formally: $c3^c = \{\geq 2 \text{ wrong} \}$. **Summary:** - $c1^c$: Not exactly one correct answer (0 or ≥2 correct). - $c2^c$: Less than two correct answers (0 or 1 correct). - $c3^c$: More than one wrong answer (≥2 wrong).