Courses / Mathematics / Probability, uncertainty and expected outcomes / Project Build and defend your work Explain a decision under uncertainty Build a fictional decision model with an explicit outcome space, conditional probabilities and numerical consequences. Compare alternatives using expected outcomes while explaining a downside that the average hides.
Choose an audience, investigate alternatives, copy evidence from your experiments, and produce an artifact. You can open this project at any time. Reports, numerical transfer checks and human review are separate outcomes.
Your project workspace Choose the kind of work you want to produce School investigation College investigation Workplace application Design a fictional fair game or travel decision. List outcomes, calculate probabilities and explain the difference between possible and expected results.
1. Collect and compare evidence Required experiment sources:
Include every source above and at least one pair with different inputs from the same experiment. Explain confounding changes yourself; the presence check does not judge your interpretation.
Open an experiment and change an input or capture a trial to make evidence available here.
2. Write and revise your report Outcome space and assumptions Define outcomes, how they are counted, whether order matters and why any equal-likelihood assumption is reasonable.
Joint and conditional calculation Show a frequency table or tree. Name every denominator and explicitly justify any independence assumption.
Random variable and expected result Assign numerical consequences, compute their weighted mean and a variation or downside measure.
Counterexample and sensitivity Change a base rate or dependence assumption and show how the recommendation changes; include a zero-probability boundary if relevant.
Recommendation and uncertainty Give a supported choice, explain why the average is not a guarantee and identify evidence needed to replace assumptions.
Your artifact: code, analysis, prototype or decision brief This field stores up to 12,000 characters of inert text. Code runs only through the explicit bounded editor in the relevant lessons; project attachments never execute.
Load a text artifact Review your work against the rubric Outcomes are counted consistently with order and replacement rules. Probabilities are valid and exhaustive where claimed; conditional denominators are explicit. Independence is justified rather than inferred from event names. Expectation and variance use outcomes and probabilities correctly and retain their units. The decision considers downside and model uncertainty rather than treating a mean as guaranteed. 11 evidence requirements remain Capture evidence from Count teams and ordered roles. Capture evidence from Check whether conditioning changes a probability. Capture evidence from Reverse a probability question. Capture evidence from Average outcomes before they happen. Include two different input configurations from the same experiment to compare. Write your outcome space and assumptions. Write your joint and conditional calculation. Write your random variable and expected result. Write your counterexample and sensitivity. Write your recommendation and uncertainty. Add your project artifact: code, analysis, prototype or decision brief. Record my report Download report and evidence Editing the report or evidence returns it to draft. Recording verifies field presence and input comparisons, not correctness of your reasoning or code.
3. Check transfer to unfamiliar cases These authored cases use different numbers or conditions from the lesson practice. They are public local checks, not secure certification. Each case permits three submissions. Opening, first responses and attempt counts survive imports; no reset creates fresh evidence.
Case prob-teams Open case prob-teams Case prob-joint Open case prob-joint Case prob-bayes Open case prob-bayes Case prob-expectation Open case prob-expectation
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