law of averages

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As a sample size increases so the data will increasingly resemble the population being sampled and will take on its characteristics (see laws of large numbers). However, there is nothing deterministic about this process. It is easy to be deluded by the gambler's fallacy, which advocates betting on numbers that ‘should have come up’. As an example, suppose that a fair die is rolled 24 times and no six is obtained. According to the gambler's fallacy a six is long overdue and must be a good bet for the 25th roll—the truth is that its probability will be the same as for every other roll, namely, 1/6.

Subjects: Probability and Statistics.

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