Let's break down the problem step by step: ### **Given Information** - A number cube (die) with faces labeled 1 to 6 is rolled. - **Event A:** The number rolled is even. - **Event B:** The number rolled is less than 4. #### **List of possible outcomes when rolling a die:** \(\{1, 2, 3, 4, 5, 6\}\) --- ### **Step 1: Write out each event** #### **Event A (even numbers):** - Even numbers between 1 and 6: **2, 4, 6** - So, \(A = \{2, 4, 6\}\) #### **Event B (numbers less than 4):** - Numbers less than 4: **1, 2, 3** - So, \(B = \{1, 2, 3\}\) --- ### **Step 2: Answer each part** #### **(a) Event "A and B" (\(A \cap B\)):** - This means the outcome is in both A **and** B. - Intersection: What numbers are both even and less than 4? - \(A \cap B = \{2\}\) #### **(b) Event "A or B" (\(A \cup B\)):** - This means the outcome is in A **or** B (or both). - Union: Combine all numbers in A and B (no repeats). - \(A \cup B = \{1, 2, 3, 4, 6\}\) #### **(c) Complement of event A (\(A'\)):** - All outcomes **not** in A. - A = \{2, 4, 6\}, so complement is \{1, 3, 5\} --- ## **Final Answers** **(a) Event "A and B":** \[\{2\}\] **(b) Event "A or B":** \[\{1, 2, 3, 4, 6\}\] **(c) The complement of the event A:** \[\{1, 3, 5\}\]