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{"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}, "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": "When we flip an unbiased coin there are two possible events that we could measure: the coin lands on heads or the coin lands on tails.

\nEach toss of the coin is independent; if we flip a coin once and it lands on heads then the next time we flip the coin it is still equally likely to land on either heads or tails.

\nIt doesn't matter what the coin landed on previously as this outcome does not affect the outcome of the next flip of the coin.

\nEven when we flip an unbiased coin $\\var{no_flips}$ times and it lands on heads each time; the next time we flip the coin, it is still equally likely to land on either heads or tails.

\nSo the probability that the coin lands on heads the next time that the coin is flipped is still $\\displaystyle\\frac{1}{2}$.

\n", "variables": {"no_flips": {"description": "Number of flips of the coin

", "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": "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?

", "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": "Previous throws don't affect the probability distribution of subsequent throws. Believing otherwise is the gambler's fallacy.

"}, "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/"}]}