# PWR-127 — Belief updating: learner worksheet Release: Revision 7T · Full Tutorial Edition Estimated time: Estimated 26 min reading and worksheet pass Difficulty: Intermediate Equipment: Basic stationery or digital tools — Four fictional urn scenarios with priors, possible urns and sequential evidence cards.; Prior–evidence–update log, calculator and formula card: prior odds = p/(1−p); likelihood ratio LR = P(evidence|A)/P(evidence|B); posterior odds = prior odds × LR; posterior probability = posterior odds/(1+posterior odds).; Alternative-explanation and future-reversal fields. Space: Desk / seated Automated structural checklist: 10 of 10 structural checks present Evidence quality/context: G1; Focused research depth Automated method-quality band: Comprehensive 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 Belief updating is changing a prior confidence state after evidence. This lesson uses a fictional urn with coloured tokens and known evidence reliability. The learner writes a prior range and change rule, reveals one card at a time, records each update, checks alternatives and compares with a Bayesian benchmark—a calculation that combines the starting odds with how expected the evidence is under each option. It never targets real political, medical, identity or interpersonal beliefs. Target outcome: The learner completes four fictional evidence sequences and makes directionally correct, proportionate updates that track the supplied likelihood information. ### Authority and setup conditions - Mark the claim fictional and define what probability refers to. - Write the prior before revealing evidence. - State what evidence would move confidence up, down or not at all. ### Required or supplied materials - Four fictional urn scenarios with priors, possible urns and sequential evidence cards. - Prior–evidence–update log, calculator and formula card: prior odds = p/(1−p); likelihood ratio LR = P(evidence|A)/P(evidence|B); posterior odds = prior odds × LR; posterior probability = posterior odds/(1+posterior odds). - Alternative-explanation and future-reversal fields. ## 1. Write the prior range Record the starting probability as a point or honest range and cite the supplied base rate. Why: A visible prior prevents hindsight and shows how far evidence moved belief. Success check: The prior and reason are fixed before card one. Accessible alternative: Complete the same research action — “Record the starting probability as a point or honest range and cite the supplied base rate.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “The prior and reason are fixed before card one.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 2. Translate the prior into counts Represent the starting probability as expected cases out of 100, split between the two urn options. Keep the original percentage beside it. Why: Concrete counts make later evidence changes visible without requiring formula fluency. Success check: The frequency table totals 100 and matches the declared prior before any evidence card opens. Accessible alternative: Complete “Represent the starting probability as expected cases out of 100, split between the two urn options. Keep the original percentage beside it.” in shorter passes, or use keyboard input, dictation or a support person, while preserving this success check: “The frequency table totals 100 and matches the declared prior before any evidence card opens.” Allow calculator support and extra time while preserving reveal order. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 3. Predeclare update direction For each possible evidence type, state whether it would be more expected if the claim were true, false or equally expected. Why: Likelihood direction matters more than whether evidence sounds impressive. Success check: Each card type has an expected direction before reveal. Accessible alternative: Complete the same research action — “For each possible evidence type, state whether it would be more expected if the claim were true, false or equally expected.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “Each card type has an expected direction before reveal.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 4. Reveal one card Open only the next card, record its reliability and alternative way it could arise, then update once. Why: Sequential logging prevents the final story from erasing intermediate reasoning. Success check: The log shows card, reliability, alternative and new probability. Accessible alternative: Complete the same research action — “Open only the next card, record its reliability and alternative way it could arise, then update once.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “The log shows card, reliability, alternative and new probability.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 5. Match update to diagnosticity Move more for evidence with a larger true-versus-false likelihood difference and little for weak or equally likely evidence. Why: Proportionate updating avoids all-or-nothing belief swings. Success check: The update size is justified by supplied likelihoods. Accessible alternative: Complete the same research action — “Move more for evidence with a larger true-versus-false likelihood difference and little for weak or equally likely evidence.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “The update size is justified by supplied likelihoods.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 6. Check cumulative coherence After all cards, ask whether any evidence was double-counted or depended on an earlier card. Why: Correlated evidence can create false certainty. Success check: Dependencies are marked and duplicates are not counted twice. Accessible alternative: Complete the same research action — “After all cards, ask whether any evidence was double-counted or depended on an earlier card.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “Dependencies are marked and duplicates are not counted twice.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 7. Plot the update path Place the prior and every revised probability on one 0–100 line, annotate the evidence card and mark any all-or-nothing jump. Why: A trajectory makes disproportionate or directionally inconsistent updates easier to inspect than the final estimate alone. Success check: Every movement has a card label, direction and magnitude, and unexplained jumps are corrected before benchmarking. Accessible alternative: Complete the same research action — “Place the prior and every revised probability on one 0–100 line, annotate the evidence card and mark any all-or-nothing jump.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “Every movement has a card label, direction and magnitude, and unexplained jumps are corrected before benchmarking.” Do not convert the research task into capability practice. Alternative relationship: Target preserving when declared check is preserved Learner notes: ________________________________________________________________________________ Completed: [ ] ## 8. Compare and set reversal evidence Calculate the Bayesian benchmark from the formula card: convert prior p to odds p/(1−p), multiply by P(evidence|A)/P(evidence|B), then convert the posterior odds O back with O/(1+O). Use only independent evidence. Explain any difference from the intuitive update and write what future card would move the belief back. Why: A benchmark teaches the normative structure while preserving uncertainty and reversibility. Success check: Final estimate, benchmark, discrepancy and reversal condition are recorded. Accessible alternative: Complete the same research action — “Calculate the Bayesian benchmark from the formula card: convert prior p to odds p/(1−p), multiply by P(evidence|A)/P(evidence|B), then convert the posterior odds O back with O/(1+O). Use only independent evidence. Explain any difference from the intuitive update and write what future card would move the belief back.” — using speech-to-text, text-to-speech, enlarged text, keyboard-only navigation, shorter work blocks or a support person. Preserve this declared check: “Final estimate, benchmark, discrepancy and reversal condition are recorded.” Do not convert the research task into capability practice. 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.