Question

1. jack tossed a coin three times. which tree - diagram shows all of the possible outcomes of the coin landing heads up or tails up?
2. a teacher has a container of paper clips. she will randomly select one paper clip from the container box:

• 8 pink clips
• 14 purple clips
• 12 yellow clips

Explanation:

Step1: Count total possible outcomes

When tossing a coin 3 times, each toss has 2 outcomes. Total outcomes: $2 \times 2 \times 2 = 8$. A valid tree diagram must have 8 end nodes.

Step2: Check branch consistency

Each first toss branch (Heads/Tails) must split into 2 branches (Heads/Tails) for the second toss, and each of those splits into 2 for the third toss. The top-left diagram (labeled F) starts with Heads, splits into Heads/Tails, each of those splits into Heads/Tails, creating all 8 unique sequences: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Step3: Eliminate invalid diagrams

• The diagram starting with Tails (G) only shows 4 outcomes, missing sequences starting with Heads.
• The pair of diagrams (H) splits outcomes into two separate trees, which is not a single complete tree diagram.
• The bottom diagram (J) has duplicate/incorrect branches (e.g., Tails leading to two Heads branches), missing valid sequences.

Answer:

F. The top-left tree diagram starting with "Heads" that branches to show all 8 possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT