Build a complete sample space
See this course’s project requirements
A chance-model packet with a complete sample space, combined-event calculations, conditional probabilities and a repeated-trial comparison.
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What to include
- List a complete equal-outcome sample space.
- Calculate a complement and an independent combined event.
- Audit overlap in an inclusive-or event.
- Compare conditional and unrestricted denominators.
- Explain observed frequency versus theoretical chance with all six changed cases.
Review and revise
Use these criteria to check your work and choose what to improve.
- Method: applies the course-specific rules to the supplied cases with visible intermediate work.
- Accuracy: results agree with the stated facts, units, boundaries and independent checks.
- Reasoning: explains why the result follows and identifies a limitation or unresolved question.
- Transfer: completes changed cases and revises the final project when a relevant assumption changes.
Want more background?
The idea in everyday life
Case: one fair coin and one fair three-sector spinner labeled 1,2,3; independent mechanisms. Outcomes record coin then spinner.
A sample space lists all possible outcomes under a stated model. Counts become probabilities only when outcomes are equally likely. Define the experiment and the outcome being counted before dividing.
Build a complete sample space — worked practice
A sample space lists all possible outcomes under a stated model. Counts become probabilities only when outcomes are equally likely. Define the experiment and the outcome being counted before dividing.
Case: one fair coin and one fair three-sector spinner labeled 1,2,3; independent mechanisms. Outcomes record coin then spinner.
Original practice material
Paste at A1.
| AMaterial | BSupplied text |
|---|---|
| Case | Case: one fair coin and one fair three-sector spinner labeled 1,2,3; independent mechanisms. Outcomes record coin then spinner. |
Copy as plain text
1. 1. List
Pair each coin side with each spinner number.
You should see: H 1, H 2, H 3, T 1, T 2, T 3.
2. 2. Count
Check that all pairs appear once.
You should see: Six equally likely outcomes.
3. 3. Select
List outcomes with heads and spinner number 2.
You should see: H 2 only.
4. 4. Calculate
Divide favorable outcomes by all equally likely outcomes.
You should see: Probability 1/6.
What to finish
A complete sample-space list with one favorable-event probability.
Watch for this
The simple count rule assumes equal likelihood. Unequal areas require appropriate probability weights rather than equal sector counts.
How can I tell I understand it?
Construct a changed paired sample space without treating unequal sectors as equally likely.
Quick knowledge check
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Source & access notes · checked 2026-10-01
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