Final answer:
To solve a 3 set Venn diagram, draw three overlapping circles within a rectangle representing the sample space, label each region with the appropriate probabilities, and ensure the total probability is 1. Overlap indicates intersection (AND events), while unions (OR events) require summing individual probabilities and subtracting intersections.
Step-by-step explanation:
How to Solve 3 Set Venn Diagrams
To solve problems involving 3 set Venn diagrams, you'll typically follow these steps:
- Draw a rectangle to represent the sample space.
- Inside the rectangle, draw three overlapping circles or ovals to represent the three sets.
- Label each part of the diagram clearly, including individual sets, their intersections (AND events), and unions (OR events).
- When given probabilities, start by labeling the overlapping sections, which represent the intersection of all three sets.
- Work outward from the intersection, filling in the probabilities for each of the seven possible regions (each individual set, each pair's intersection, and the intersection of all three).
- Ensure the sum of the probabilities adds up to 1, representing the entire sample space.
For example, if you have events C, P, and a third event, such as event T, you would first figure out C AND P AND T. After that, address C AND P, C AND T, and P AND T. Finally, fill in the individual probabilities for C, P, and T that are not part of any intersection.
Remember, the overlap indicates where multiple sets intersect and contains elements common to all overlapping sets. Calculating probabilities for unions (OR events) involves adding together probabilities of individual events and subtracting the probabilities of intersections to avoid double-counting.
For questions asking about conditional probabilities, like the probability of belonging to a club given that the student works part time, use the formula for conditional probability, which relates the probability of intersections to the probability of the given event.