Sample spaces
Objective. List outcomes systematically for combined experiments.
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- 2. Worked example
- 3. Practice
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Learn: the key idea
A sample space lists every possible outcome of one or more combined experiments, such as tossing two coins or rolling two dice, and is often organised as a list or a grid for clarity. Listing systematically, such as in alphabetical or numerical order, avoids missing or repeating outcomes. For two independent events, the total number of outcomes equals the number of outcomes of the first multiplied by the number of outcomes of the second. Example: tossing a coin (2 outcomes) and rolling a die (6 outcomes) gives a sample space of 2 × 6 = 12 total outcomes.
Worked example
A spinner has 3 equal sections labelled A, B, C, and a coin is tossed. Find the total number of outcomes in the sample space.
- 1The spinner has 3 possible outcomes: A, B or C.
- 2The coin has 2 possible outcomes: Heads or Tails.
- 3Multiply the number of outcomes for each event: 3 × 2.
- 4The sample space contains 6 total outcomes.
Answer: 6
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Practice
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Start practisingCommon mistake. Pupils often list outcomes like (Heads, 1) and (1, Heads) as different when order of recording doesn't change the combined event meaning; use a consistent systematic order, such as always coin first, to avoid confusion or repeats.
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