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{"name": "SA15 Intuitive Probability", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "SA15 Intuitive Probability", "tags": ["taxonomy"], "metadata": {"description": "<p>Predicting the probability of an unbiased coin landing on heads based on the results of previous throws.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "<p>When we flip an unbiased&nbsp;coin there are two possible events that we could measure: the coin lands on heads or&nbsp;the coin lands on tails.</p>\n<p>Each toss of the coin is independent; if we flip a coin once and it lands&nbsp;on heads then the next time we flip the coin it is still equally likely to land on either heads or tails.</p>\n<p>It doesn't matter what the coin landed on previously as this&nbsp;outcome does not affect the&nbsp;outcome of the next flip of the coin.</p>\n<p>Even when we flip&nbsp;an unbiased coin&nbsp;$\\var{no_flips}$ times and it lands on&nbsp;heads each time; the next time we flip the coin, it is still equally likely to land on either heads or tails.</p>\n<p>So the probability that the coin lands on heads the next time that the coin is flipped is still $\\displaystyle\\frac{1}{2}$.</p>\n<h4 style=\"text-align: center;\"><a href=\"https://www.sheffield.ac.uk/mash/stats-resources/probability#equally-likely-outcomes\" target=\"_blank\" rel=\"noopener\">Use this link to find some resources which will help you revise this topic.</a></h4>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"no_flips": {"name": "no_flips", "group": "Ungrouped variables", "definition": "random(6..9)", "description": "<p>Number of flips of the coin</p>", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["no_flips"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>An unbiased coin is flipped $\\var{no_flips}$ times. Given that the coin landed on heads each time, what is the probability of the coin landing on heads the next time it is flipped?</p>", "minValue": "1/2", "maxValue": "1/2", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Upuli Wickramaarachchi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23527/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Upuli Wickramaarachchi", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23527/"}, {"name": "Michael Pan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/23528/"}]}