The target compound-event probability is \(1/6\). Evaluate Cases 1–6, then report the \(\text{complete}~\text{matching}~\text{set}\).
Case 1. A \(3\text{-}\text{section}\) spinner is followed by a fair \(1\text{--}6\) cube; the event is blue and \(4\).
Case 2. A bag has \(2\) red and \(4\) yellow marbles, then a fair coin is flipped; the event is red and heads.
Case 3. A lunch uses \(1~\text{of}~2~\text{sandwiches}\) and \(1~\text{of}~3~\text{drinks}\); the event is turkey and juice.
Case 4. A fair coin is followed by a fair \(1\text{--}3\) cube; the event is tails and \(2\).
Case 5. A code uses \(1~\text{of}~\text{four}~\text{letters}~{A,~B,~C,~D}\) and \(1~\text{of}~\text{two}~\text{digits}~{1,~2}\); the event is \(C_{2}\).
Case 6. A tree has \(2~\text{equal}~\text{first}~\text{branches}\) and \(3~\text{equal}~\text{second}~\text{branches}\) from each, with \(\text{exactly}~1~\text{of}~6~\text{outcomes}~\text{favorable}\).
What this problem is really about
Evaluate all six cases by the full two-stage event, not by a promising first step. Multiply the stage probabilities when they are independent, or count favorable leaves over total equal leaves when an organizer is given, then compare the reduced result with the target. This common test handles spinners, bags, menus, codes, and trees without changing the meaning of probability.