Listing outcomes systematically

OCR J560 expects students to enumerate possibilities without missing or duplicating any. The three core tools are sample-space tables, two-way tables/grids, and Venn diagrams.

Sample-space diagrams (grids)

For two events, list outcomes of one along the top and the other down the side, then fill the body with the joint outcome.

Example: rolling two fair dice and summing.

	1	2	3	4	5	6
1	2	3	4	5	6	7
2	3	4	5	6	7	8
3	4	5	6	7	8	9
4	5	6	7	8	9	10
5	6	7	8	9	10	11
6	7	8	9	10	11	12

36 equally likely outcomes. P(sum = 7) = 6/36 = 1/6.

Two-way tables

Used when the data are categorical (e.g. gender × subject choice). Rows total + column totals must each match the grand total.

Venn diagrams (Higher mainly, also extended Foundation)

Two-set Venn: circles A and B inside a rectangle (universal set ξ).

• A only: in A but not B.
• B only: in B but not A.
• A ∩ B: in BOTH (the overlap).
• A ∪ B: in EITHER (the whole shaded region).
• (A ∪ B)' = neither: outside both circles.

Three-set Venn (Higher): A, B, C with seven internal regions plus the outside.

Set notation

Symbol	Meaning
ξ	Universal set
A ∪ B	A union B (in A OR B OR both)
A ∩ B	A intersection B (in BOTH)
A'	Complement of A (NOT in A)
n(A)	Number of elements in A
∅ or { }	Empty set

Combinations vs permutations (informal at GCSE)

OCR doesn't formally test nCr / nPr, but expects systematic listing. For "how many ways to pick 2 from {A, B, C}": list AB, AC, BC = 3 ways.

OCR mark scheme conventions

• B1 for a complete table/diagram with all values correct.
• M1 for using the diagram to extract the relevant count.
• A1 for the probability/answer.
• For Venn shading: B1 for shading exactly the right region.