1. **State the problem:** We want to find all possible outcomes of answering a quiz with five true/false questions. 2. **Understanding the problem:** Each question has 2 possible answers: True (T) or False (F). 3. **Formula used:** The total number of ways to answer is given by the number of outcomes per question raised to the power of the number of questions: $$\text{Total outcomes} = 2^5$$ 4. **Calculate:** $$2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32$$ 5. **Explanation:** This means there are 32 different ways to answer the five questions. 6. **List of outcomes:** Each outcome is a sequence of 5 letters, each either T or F. For example: - T T T T T - T T T T F - T T T F T - ... (and so on until all 32 combinations are listed) 7. **Tree diagram:** - Start with a single node. - From this node, branch into 2 nodes labeled T and F for question 1. - From each of those nodes, branch again into T and F for question 2. - Repeat this branching for all 5 questions. - Each path from the root to a leaf node represents one unique sequence of answers. This tree will have 5 levels (one for each question) and $2^5=32$ leaf nodes representing all possible answer combinations.