// Numbas version: finer_feedback_settings
{"name": "The gambler's fallacy - probability of getting heads again after repeatedly getting heads", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "The gambler's fallacy - probability of getting heads again after repeatedly getting heads", "variablesTest": {"condition": "", "maxRuns": 100}, "type": "question", "tags": ["taxonomy"], "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></h4>", "variables": {"no_flips": {"description": "<p>Number of flips of the coin</p>", "name": "no_flips", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(6..9)"}}, "extensions": [], "statement": "", "variable_groups": [], "parts": [{"correctAnswerFraction": true, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "notationStyles": ["plain", "en", "si-en"], "maxValue": "1/2", "showFeedbackIcon": true, "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>", "correctAnswerStyle": "plain", "allowFractions": true, "mustBeReduced": false, "minValue": "1/2", "variableReplacements": [], "marks": 1, "showCorrectAnswer": true}], "ungrouped_variables": ["no_flips"], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Previous throws don't affect the probability distribution of subsequent throws. Believing otherwise is the gambler's fallacy.</p>"}, "preamble": {"css": "", "js": ""}, "functions": {}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}