Law of Truly Large Numbers

From Wikipedia, the free encyclopedia

The Law of Truly Large Numbers, attributed to Persi Diaconis and Frederick Mosteller, states that with a sample size large enough, any outrageous thing is likely to happen.^[1] Because we never find it notable when the likely thing happens, we highlight unlikely events and notice them more. It seeks to debunk one element of supposed supernatural phenomenology.

Contents 1 Example 2 In pseudoscience 3 See also 4 Notes 5 References 6 External links

[edit] Example

For a simplified example of the law, assume that a given event happens with a probability of 0.1% in one trial. Then the probability that this unlikely event does not happen in a single trial is 99.9% = 0.999.

In a sample of 1000 independent trials, the probability that the event does not happen in any of them is 0.999¹⁰⁰⁰, a probability of 36.8%. The probability that the event happens at least once in 1000 trials is then 1 − 0.368 = 0.632 or 63.2%. The probability that it happens at least once in 10,000 trials is even 1 − 0.999¹⁰⁰⁰⁰ = 0.99995 = 99.995%.

This means that this "unlikely event" has a probability of 63.2% of happening if 1000 chances are given, or even over 99.9% for 10,000 chances. In other words, even given a highly unlikely event, the chance that it never happens, given enough tries, is even more unlikely.

[edit] In pseudoscience

The law comes up in pseudoscience and is sometimes called the Jeane Dixon effect (see also Postdiction). It holds that the more predictions a psychic makes, the better the odds that one of them will "hit". Thus, if one comes true, the psychic expects us to forget the vast majority which did not happen.

Humans can be susceptible to this fallacy. A similar manifestation can be found in gambling, where gamblers tend to remember their wins and forget their losses and thus hold an inflated view of their real winnings.

[edit] See also

• Coincidence
• Large numbers
• Law of large numbers
• Law of small numbers
• Littlewood's law
• Miracle
• Psychic phenomena
• Infinite monkey theorem

[edit] Notes

[edit] References

• Weisstein, Eric W., "Law of Truly Large Numbers" from MathWorld.
• Diaconis, P.; Mosteller, F. (1989). "Methods of Studying Coincidences". Journal of the American Statistical Association 84 (408): 853–861. JSTOR 2290058. MR1134485. http://stat.stanford.edu/~cgates/PERSI/papers/mosteller89.pdf. Retrieved 2009-04-28. 
• Everitt, B.S. (2002) Cambridge Dictionary of Statistics, 2nd Edition, CUP. ISBN 0-521-81099-x

[edit] External links

• skepdic.com on the Law of Truly Large Numbers
• on the Law of Truly Large Numbers