What you’ll learn
List sample spaces.
Key idea
A complete sample space pairs every first-stage possibility with every second-stage possibility without merging their labels.
Distinct pairs can have equal sums; listing outcomes alone does not imply uniform probability.
Worked example
Enter the exact value or ordered values in the format requested below.
Two stages allow first labels [2, 3] and second labels [0, 1, 2]. Every ordered pair is possible. Enter the number of distinct complete outcomes.
- Each first-stage label [2, 3] pairs with every second-stage label [0, 1, 2], retaining order.
- The complete space is {(2,0),(2,1),(2,2),(3,0),(3,1),(3,2)}, with 2×3=6 distinct pairs; a sum can merge different ordered pairs.
Answer: 6
Quick Check
Interpret the result of 'List sample spaces' in the data-generating context, including units and population limits.
For first-stage labels [1, 2, 3] and second-stage labels [1, 2], interpret the complete ordered sample-space list, retaining first-then-second positions.