Final answer:
A Venn diagram is used to represent the probabilities of different events in a sample space. The Venn diagram includes all possible outcomes, and the probabilities within its sections must sum up to 1. To calculate probabilities involving combined events, we consider both the individual event probabilities and their intersection.
Step-by-step explanation:
When creating a Venn diagram to represent events in probability, we typically start by drawing a rectangle that signifies the sample space. Inside this rectangle, we draw circles or ovals for each event. For events that can occur simultaneously, their circles or ovals will overlap. The probabilities within each section of a Venn diagram must add up to 1, since they represent all possible outcomes.
To answer the student's questions based on the given probabilities:
- Probability of belonging to a club (represented by C): 0.40 or 40%.
- Probability of working part-time (represented by PT): 0.50 or 50%.
- For the overlapping section, representing students who both belong to a club and work part-time, the probability is 0.05 or 5%.
- To find the probability that a student belongs to a club or works part-time, we add the probabilities of each event and then subtract the overlap: 0.40 + 0.50 - 0.05 = 0.85 or 85%.
The special case of the overlapping area could represent, for example, students who purchase both novels and nonfiction books, belong to both the Computer and Spanish Clubs, or possess any two combined characteristics being analyzed.