Probability Systems (Extended)

Organising Outcomes Systematically

As probability problems grow in complexity, informal listing becomes unreliable. This topic equips Extended students with systematic methods for counting and organising outcomes — the foundation for working with permutations and combinations.

Systematic Listing

Systematic listing ensures no outcomes are missed or duplicated. Techniques include:

• Sample space diagrams (grids): Ideal for two-event problems with equally likely outcomes
• Organised lists: Using alphabetical or numerical order to track all combinations
• Tree diagrams: Useful when events happen in sequence and outcomes differ at each stage

Introduction to Permutations and Combinations

Permutations

A permutation is an arrangement where order matters. For example, the number of ways to arrange 3 books from a shelf of 5 is a permutation problem. The notation P(n, r) or nPr is used.

Combinations

A combination is a selection where order does not matter. Choosing 3 students from a class of 20 to form a committee is a combination problem. The notation C(n, r), nCr, or (n choose r) is used.

At MYP Extended level, questions focus on recognising whether order matters and applying the correct counting principle rather than deriving formulas from first principles.

Common Mistakes

• Treating a combination as a permutation (or vice versa) by not reading the context carefully
• Missing outcomes when listing systematically due to an unstructured approach
• Confusing the total number of arrangements with the number of favourable ones