Possibility spaces

A possibility space (also called a sample space) is a complete list of all possible outcomes of an experiment. OCR J560 tests this on probability questions across all six papers.

Single events

For a single fair experiment, the possibility space lists every outcome.

• Coin: {H, T}
• Six-sided die: {1, 2, 3, 4, 5, 6}
• Spinner with 4 equal sectors A, B, C, D: {A, B, C, D}

If outcomes are equally likely, P(event) = (favourable outcomes) / (total outcomes).

Combined experiments — two events

When two experiments happen together, the possibility space is the product of the two — every pair of outcomes.

Example: flip a coin AND roll a die.

• Possibility space: {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}.
• 12 equally likely outcomes.

Building grids systematically

For two events with outcomes A_i and B_j, draw a grid: A across the top, B down the side. Each cell is one combined outcome.

Example: spin a 3-spinner (R, G, B) and flip a coin.

	R	G	B
H	HR	HG	HB
T	TR	TG	TB

6 outcomes. P(green and tails) = 1/6.

Tree diagrams (Higher; also Foundation extension)

When events are sequential and outcomes have different probabilities, a tree diagram is clearer:

• Each branch shows an outcome with its probability.
• Probability of a path = product of branch probabilities along it.
• Total of all path probabilities = 1.

Listing outcomes systematically

Always work in a fixed order to avoid duplicates. For "pick 2 letters from {A, B, C}":

• AB, AC, BC (3 unordered pairs).
• AB, BA, AC, CA, BC, CB (6 ordered pairs).

OCR mark scheme conventions

• B1 for a complete and correct sample space.
• M1 for identifying the favourable outcomes.
• A1 for the probability as a fraction in simplest form.
• B1 (often) for marking outcomes systematically (e.g. all pairs in alphabetical order).