Introduction to Probability Diagrams
Probability problems often become much clearer when you have a visual tool to organise information. In IB Math AA SL, you are expected to work confidently with three main types of probability diagrams:
- Venn diagrams , for showing relationships between sets of events
- Tree diagrams , for sequential events and conditional probabilities
- Sample space diagrams , for listing all possible outcomes of two or more events
Choosing the right diagram depends on the structure of the problem. As you work through this subtopic, you will also encounter the key concepts of combined events, mutually exclusive events, conditional probability, and independent events , all of which connect directly to these visual tools.
Before starting any probability problem, ask yourself: Are the events happening at the same time or one after another? Are they related to each other? Your answers will guide which diagram and which formula to use.
Venn Diagrams
Venn Diagram: A diagram that uses overlapping circles inside a rectangle (the sample space) to represent events and their relationships. The rectangle represents all possible outcomes, and each circle represents an event.
The intersection is the region where both circles overlap , it contains outcomes that belong to both events A and B. The union covers everything inside either circle.
In a class, 65% of students play soccer, 45% play basketball, and 25% play both.
Step 1: Identify regions from the inside out.
- (both sports , the innermost region)
- Soccer only:
- Basketball only:
- Neither:
Step 2: Check the union.
This confirms:
Always fill in a Venn diagram starting from the innermost region (the intersection) and work outwards. This avoids double-counting and makes finding each region straightforward , no complicated algebra needed.
