1. The problem is to understand and use Venn diagrams and tree diagrams to represent sets and probabilities. 2. A Venn diagram visually shows the relationships between different sets using overlapping circles. Each circle represents a set, and overlaps represent intersections. 3. A tree diagram is a branching diagram that shows all possible outcomes of an event or sequence of events, useful for calculating probabilities. 4. For example, if you have two sets A and B, the Venn diagram shows: - $A \cap B$ (intersection) - $A \cup B$ (union) - $A^c$ and $B^c$ (complements) 5. In a tree diagram, each branch represents a choice or event, and the paths represent combined outcomes. Probabilities along branches multiply to find joint probabilities. 6. To solve problems, identify the sets or events, draw the Venn or tree diagram accordingly, and use set or probability rules: - $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ - $P(A \cap B) = P(A) \times P(B|A)$ for dependent events 7. These diagrams help visualize and calculate probabilities or set relationships clearly and systematically.