// Numbas version: exam_results_page_options {"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.

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Each 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.

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

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Even 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.

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

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Number of flips of the coin

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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?

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

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