Possibility spaces

A possibility space is a complete list of every equally-likely outcome of an experiment. Edexcel uses them as the basis for finding probabilities by counting favourable outcomes.

Single experiment

Rolling a fair six-sided dice: possibility space = {1, 2, 3, 4, 5, 6}, six equally likely outcomes.

P(even) = 3/6 = 1/2.

Combined experiments — sample space diagrams

For two stages (e.g. roll two dice, flip two coins), draw a sample space diagram (a grid) listing one experiment along the rows, the other along the columns. Each cell holds the combined outcome.

Example: roll two fair dice, find the sum.

	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

There are 36 cells, each equally likely.

• P(sum = 7) = 6/36 = 1/6.
• P(sum is prime) = count of 2, 3, 5, 7, 11 = 1 + 2 + 4 + 6 + 2 = 15. P = 15/36 = 5/12.
• P(sum > 9) = sum of 10, 11, 12 cells = 3 + 2 + 1 = 6. P = 6/36 = 1/6.

Listing for combined experiments

If the cells become unwieldy, list outcomes as ordered pairs.

Example: flip a coin and roll a 4-sided dice. Possibility space = {(H,1), (H,2), (H,3), (H,4), (T,1), (T,2), (T,3), (T,4)} — 8 outcomes.

Equally likely vs not

Possibility-space counting only works if every cell is equally likely. For biased dice, weighted spinners, or non-equally-likely outcomes, you must use probability trees (P9 territory) instead.

Common Edexcel exam tip

For "find the probability that …" questions, set out the sample space M1 before identifying the favourable cells M1. Then write the fraction with both numerator and denominator A1. Skipping the diagram and writing only the final fraction risks losing 2 marks if it is wrong.