What is important to know about Combined events & sample space?

A sample space lists all possible outcomes of an experiment.

For two dice or two spinners, use a grid (sample space diagram) to list all outcomes.

P(event) = number of favourable outcomes ÷ total number of outcomes.

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Statistics & Probability · Foundation & Higher

Combined events & sample space

When two events happen together, you list all possible outcomes in a sample space diagram. You use this to find probabilities of combined events.

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1A sample space lists all possible outcomes of an experiment.
2For two dice or two spinners, use a grid (sample space diagram) to list all outcomes.
3P(event) = number of favourable outcomes ÷ total number of outcomes.
4Outcomes in a sample space are all equally likely (assuming fair dice, coins etc.).
5P(A and B) = P(A) × P(B) only if A and B are independent events.

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Example 1

Two fair dice are rolled. Find the probability that the sum equals 7.

Working

Answer1/6

Example 2

A coin is flipped and a fair 4-sided die is rolled. List the sample space and find P(H and even number).

Working

Answer1/4

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✗Listing some outcomes twice or missing some — use a systematic grid.

✗Not recognising that all outcomes in a fair sample space are equally likely.

✗Confusing "and" (both events occur) with "or" (at least one occurs).

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✓Draw a sample space grid for two-event problems — it prevents missing outcomes.

✓Count outcomes carefully: mark the favourable ones before dividing.

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