Definition: The sample space of an experiment is the set of all possible outcomes, which can be listed, shown in a table, or drawn as a tree diagram.
What is a sample space?
It is the complete list of results an experiment could have. Spin a spinner with sections A, B, C and the sample space is {A, B, C}.
How do you list it for several steps?
Use an organized list, table, or tree diagram. Flip a coin, then roll a 4-sided die. The outcomes are H1, H2, H3, H4, T1, T2, T3, T4, so there are 2 x 4 = 8.
Why does it matter?
Probabilities come from counting. The chance of heads and an even number is 2 favorable outcomes (H2, H4) out of 8, or 1/4.
What is the counting shortcut?
Multiply the number of choices at each stage. A lunch with 3 sandwiches, 4 drinks, and 2 desserts gives 3 x 4 x 2 = 24 combinations.
What is a common mistake?
Missing outcomes or counting equal outcomes as one. In the sum of two dice, the sums 2 to 12 are not equally likely: there are 36 outcomes, and the sum 7 has 6 of them while the sum 2 has only 1.
Where to learn it
- Compound Events, Sample Spaces and Simulations – lesson
- Probability Models and Chance Experiments – lesson