1. The problem asks which tree diagram correctly represents the sample space of flipping a coin two times. 2. When flipping a coin twice, each flip can result in Heads (H) or Tails (T). 3. The sample space consists of all possible ordered pairs of outcomes: $\{HH, HT, TH, TT\}$. 4. A tree diagram starts with the first flip branching into H or T. 5. From each of these branches, the second flip again branches into H or T. 6. Therefore, the correct tree diagram must have the first level branches as H and T, and from each, branches to H and T. 7. Checking the options: - Diagram 1: First level branches H and T; second level branches are H and H from H, and T and T from T (incorrect, second level branches should be H and T). - Diagram 2: First level branches H and H (incorrect, should be H and T). - Diagram 3: First level branches H and T; second level branches H and T from both (correct). - Diagram 4: First level branches T and T (incorrect). 8. Thus, Diagram 3 correctly represents the sample space. Final answer: Diagram 3 is the correct tree diagram representing the sample space of flipping a coin two times.