# PWR-115 — Probabilistic reasoning: learner worksheet Release: Revision 7T · Full Tutorial Edition Estimated time: Estimated 18 min reading and worksheet pass Difficulty: Introductory Equipment: Basic stationery or digital tools — The ten benign event rows below; A natural-frequency and probability worksheet; The staged outcome-and-calculation key, kept closed until all ten probabilities are locked; A method-review sheet with largest overforecast, largest underforecast, counter-reason and next-set change Space: Desk / seated Automated structural checklist: 10 of 10 structural checks present Evidence quality/context: G1; Focused research depth Automated method-quality band: Established Method-rating basis: Structure coverage, instruction/check specificity, alternative distinctness, source troubleshooting, comparison depth and whether purpose/check fields are authored rather than derived. Editorial review: Pending manual editorial sign off ## Before you begin - [ ] I read the tutorial authority and stop conditions. - [ ] I have the required equipment/space or a declared accessible alternative. ## Canonical source context This tutorial teaches the full forecast-record cycle on ten benign fictional events. Define the event and reference class, convert favourable cases to a natural frequency, lock a probability, reveal the staged outcome, calculate the Brier score, preserve every row, inspect the direction of the largest errors and write one method update for a fresh set. The exercise is not financial, medical or safety-critical forecasting. Target outcome: Define probabilistic reasoning without inheriting mythology or broader claims. Explain what the current evidence supports and what it does not establish. Use the declared measurement boundary and recognise misleading proxies. Complete only the separately governed capability practice inside its declared limits. Make a retention, transfer, maintenance, provider or stop decision without overclaiming. ### Authority and setup conditions - Use only the fictional or mechanical events below; do not adapt the exercise to gambling, finance, medicine, safety, or another consequential decision. - Do not alter an event definition, probability, or resolution after opening its outcome. - Eight events are a calculation exercise, not a stable estimate of a person's calibration or judgement. ### Required or supplied materials - The ten benign event rows below - A natural-frequency and probability worksheet - The staged outcome-and-calculation key, kept closed until all ten probabilities are locked - A method-review sheet with largest overforecast, largest underforecast, counter-reason and next-set change ### Supplied fixture All elementary outcomes in each row are equally likely. Lock all ten forecasts before opening the staged outcome key. | Event id | Event | Reference class | Learner natural frequency | Learner probability before reveal | Learner Brier after reveal | | --- | --- | --- | --- | --- | --- | | E1 | Draw a blue tile | Bag: 3 blue, 7 white; one draw | [record] | [lock] | [calculate] | | E2 | Roll an even number | One fair six-sided die | [record] | [lock] | [calculate] | | E3 | Draw a star card | 20 cards: 5 stars, 15 circles | [record] | [lock] | [calculate] | | E4 | Land on green | 8 equal sectors: 1 green, 7 orange | [record] | [lock] | [calculate] | | E5 | Draw a red bead | Jar: 18 red, 12 yellow | [record] | [lock] | [calculate] | | E6 | Get at least one head | Two fair flips: HH, HT, TH, TT | [record] | [lock] | [calculate] | | E7 | Draw a prize ticket | 100 tickets: 2 prize, 98 non-prize | [record] | [lock] | [calculate] | | E8 | Get three heads | Three fair flips: 8 ordered outcomes | [record] | [lock] | [calculate] | | E9 | Roll a 1 | One fair ten-sided die numbered 1–10 | [record] | [lock] | [calculate] | | E10 | Draw a vowel card | 10 cards: A, E, I and seven consonants | [record] | [lock] | [calculate] | ## 1. Copy each exact event and reference class Copy each exact event and reference class. Do not replace it with a vague event such as ‘soon’ or ‘likely.’ Why: “Copy each exact event and reference class” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion. Success check: A legible entry directly completes “Copy each exact event and reference class” and records the requested condition, decision or boundary without adding a new claim. Accessible alternative: Complete “Copy each exact event and reference class. Do not replace it with a vague event such as ‘soon’ or ‘likely.’” in shorter passes, or use keyboard input, dictation or a support person, while preserving this success check: “A legible entry directly completes “Copy each exact event and reference class” and records the requested condition, decision or boundary without adding a new claim.” Use text-to-speech, enlarged text, keyboard navigation, shorter sessions, a support person or an equivalent non-practical record format as needed. Accessibility changes must not enlarge practical authority. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 2. Write favourable outcomes out of total equally likely outcomes before converting to… Write favourable outcomes out of total equally likely outcomes before converting to a decimal probability. Why: “Write favourable outcomes out of total equally likely outcomes before converting to a decimal probability” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion. Success check: A legible entry directly completes “Write favourable outcomes out of total equally likely outcomes before converting to a decimal probability” and records the requested condition, decision or boundary without adding a new claim. Accessible alternative: Complete the same research action — “Write favourable outcomes out of total equally likely outcomes before converting to a decimal probability.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “A legible entry directly completes “Write favourable outcomes out of total equally likely outcomes before converting to a decimal probability” and records the requested condition, decision or boundary without adding a new claim.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 3. For each row, write one counter-reason: a way the event could fail… For each row, write one counter-reason: a way the event could fail even when it seems plausible, or occur even when it seems unlikely. Why: “For each row, write one counter-reason: a way the event could fail even when it seems plausible, or occur even when it seems unlikely” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion. Success check: A legible entry directly completes “For each row, write one counter-reason: a way the event could fail even when it seems plausible, or occur even when it seems unlikely” and records the requested condition, decision or boundary without adding a new claim. Accessible alternative: Complete the same research action — “For each row, write one counter-reason: a way the event could fail even when it seems plausible, or occur even when it seems unlikely.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “A legible entry directly completes “For each row, write one counter-reason: a way the event could fail even when it seems plausible, or occur even when it seems unlikely” and records the requested condition, decision or boundary without adding a new claim.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 4. Lock all ten probabilities before opening any staged outcome Lock all ten probabilities before opening any staged outcome. Why: “Lock all ten probabilities before opening any staged outcome” carries the authored Probabilistic reasoning method into a reviewable output without adding an unstated task, dose or claim. Success check: Evidence of completion shows the learner followed this exact instruction without adding an unstated step: “Lock all ten probabilities before opening any staged outcome.” Accessible alternative: Complete “Lock all ten probabilities before opening any staged outcome.” in shorter passes, or use keyboard input, dictation or a support person, while preserving this success check: “Evidence of completion shows the learner followed this exact instruction without adding an unstated step: “Lock all ten probabilities before opening any staged outcome.”” Use text-to-speech, enlarged text, keyboard navigation, shorter sessions, a support person or an equivalent non-practical record format as needed. Accessibility changes must not enlarge practical authority. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 5. Reveal one outcome at a time and calculate Brier = (probability -… Reveal one outcome at a time and calculate Brier = (probability - outcome) squared. Preserve every forecast exactly as locked. Why: “Reveal one outcome at a time and calculate Brier = (probability - outcome) squared” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion. Success check: The work shows the value requested by “Reveal one outcome at a time and calculate Brier = (probability - outcome) squared”, retains the supplied units or signs and leaves any unsupported value unknown. Accessible alternative: Complete the same research action — “Reveal one outcome at a time and calculate Brier = (probability - outcome) squared. Preserve every forecast exactly as locked.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “The work shows the value requested by “Reveal one outcome at a time and calculate Brier = (probability - outcome) squared”, retains the supplied units or signs and leaves any unsupported value unknown.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 6. Add all ten Brier scores and divide by ten Add all ten Brier scores and divide by ten. Keep the individual rows; the mean does not explain the direction of an error. Why: “Add all ten Brier scores and divide by ten” isolates the named evidence distinction so the learner can interpret Probabilistic reasoning without extending the claim. Success check: The output directly answers “Add all ten Brier scores and divide by ten”, names the relevant distinction and stays within the supplied record. Accessible alternative: Complete the same research action — “Add all ten Brier scores and divide by ten. Keep the individual rows; the mean does not explain the direction of an error.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “The output directly answers “Add all ten Brier scores and divide by ten”, names the relevant distinction and stays within the supplied record.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 7. Identify the largest overforecast and largest underforecast, then write one narrow method… Identify the largest overforecast and largest underforecast, then write one narrow method update such as checking denominators before a fresh set. Why: “Identify the largest overforecast and largest underforecast, then write one narrow method update such as checking denominators before a fresh set” creates the auditable value, condition or statement needed for the tutorial’s later comparison and conclusion. Success check: A legible entry directly completes “Identify the largest overforecast and largest underforecast, then write one narrow method update such as checking denominators before a fresh set” and records the requested condition, decision or boundary without adding a new claim. Accessible alternative: Complete the same research action — “Identify the largest overforecast and largest underforecast, then write one narrow method update such as checking denominators before a fresh set.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “A legible entry directly completes “Identify the largest overforecast and largest underforecast, then write one narrow method update such as checking denominators before a fresh set” and records the requested condition, decision or boundary without adding a new claim.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 8. Use a new benign ten-event set for any later review Use a new benign ten-event set for any later review. Do not edit, delete or recycle the resolved rows. Why: “Use a new benign ten-event set for any later review” isolates the named evidence distinction so the learner can interpret Probabilistic reasoning without extending the claim. Success check: The output directly answers “Use a new benign ten-event set for any later review”, names the relevant distinction and stays within the supplied record. Accessible alternative: Complete “Use a new benign ten-event set for any later review. Do not edit, delete or recycle the resolved rows.” in shorter passes, or use keyboard input, dictation or a support person, while preserving this success check: “The output directly answers “Use a new benign ten-event set for any later review”, names the relevant distinction and stays within the supplied record.” Use text-to-speech, enlarged text, keyboard navigation, shorter sessions, a support person or an equivalent non-practical record format as needed. Accessibility changes must not enlarge practical authority. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## Reflection What changed? ________________________________________________________________________________ What remains difficult? ________________________________________________________________________________ What will I repeat, adapt, ask for help with, or stop? ________________________________________________________________________________ --- Completion of this worksheet demonstrates tutorial participation only. It does not establish capability, qualification, safety clearance, diagnosis, treatment or independent validation.