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Orders of magnitude (probability)

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This page lists events in order of increasing probability, grouped by orders of magnitude. These probabilities were calculated given assumptions detailed in the relevant articles and references. For example, the probabilities of obtaining the different poker hands assume that the cards are dealt fairly.

List of orders of magnitude for probability
Factor SI prefix Value Item
0 1.0×10−[math]\displaystyle{ n\to\infty }[/math] Almost never.
10−4.5×1029 10−4.5×1029 Probability of a human spontaneously teleporting 50 kilometres (31 miles) due to quantum effects[1]
10−360,783 1.0×10−360,783 Probability of a monkey in front of a typewriter typing Hamlet on the first try, taking punctuation, capitalization and spacing into account[2]
10−183,800 1.0×10−183,800 Rough first estimate of the probability of a monkey in front of a typewriter typing all the letters of Hamlet on the first try[3]
10−67 8.07×10−67 Probability of shuffling a standard 52-card deck in any specific order[4]
10−30 Quecto- (q) 1×10−30 One in 1,000,000,000,000,000,000,000,000,000,000
10−28 4.47×10−28 Approximate probability of all four players in a game of bridge getting a complete suit[5]
10−27 Ronto- (r) 1×10−27 One in 1,000,000,000,000,000,000,000,000,000
10−24 Yocto- (y) 1×10−24 One in 1,000,000,000,000,000,000,000,000
10−21 Zepto- (z) 1×10−21 One in 1,000,000,000,000,000,000,000
10−19 2.83×10−19 Approximate probability of matching 20 numbers for 20 in a game of keno
10−18 Atto- (a) 1×10−18 One in 1,000,000,000,000,000,000
10−16 2.74×10−16 Probability of rolling snake eyes 10 times in a row on a pair of fair dice
10−15 Femto- (f) 1×10−15 One in 1,000,000,000,000,000
10−12 Pico- (p) 1×10−12 One in 1,000,000,000,000
10−11 2.52×10−11 Approximate probability of one player in a game of bridge getting a complete suit
10−10 2.0×10−10 Probability per second of a SATA harddisk failure during an MTBF test[6]
5.25×10−10 Caesium-137 atom decay each second[7]
9.9×10−10 Gaussian distribution: probability of a value being more than 6 standard deviations from the mean on a specific side[8]
10−9 Nano- (n) 1×10−9 One in 1,000,000,000
3.9×10−9 Probability of an entry winning the jackpot in the Mega Millions multi-state lottery in the United States*[9]
5.707×10−9 Probability of winning the Grand Prize (matching all 6 numbers) in the US Powerball lottery with one ticket in January 2014
10−8 1.303×10−8 Probability of winning the Grand Prize (matching all 6 numbers) in the Australian Powerball lottery with one ticket in March 2013
2.219×10−8 odds of winning the Jackpot (matching the 6 main numbers from 59) in the UK National Lottery with one ticket since 10 October 2015
7.151×10−8 odds of winning the Jackpot (matching the 6 main numbers from 49) in the UK National Lottery with one ticket until 10 October 2015
10−7 1.17×10−7 Death per aircraft journey[10]
2.9×10−7 Gaussian distribution: probability of a value being more than 5 standard deviations from the mean on a specific side[11]
8.0×10−7 Death per person per year by lightning strike in Germany (Europe)[12]
10−6 Micro- (µ) 1×10−6 Life-threatening adverse reaction from a measles vaccine[13]
1.43×10−6 Probability of the Yellowstone supervolcano erupting in a given year.
1.5×10−6 Probability of being dealt a royal flush in poker
10−5 1.4×10−5 Probability of being dealt a straight flush (other than a royal flush) in poker
1.6×10−5 Risk that the asteroid 2013 TV135 which is 450 meters wide[14] will impact earth in 2032[15]
3.2×10−5 Gaussian distribution: probability of a value being more than 4 standard deviations from the mean on a specific side[16]
8.43×10−5 Probability of a deadly vehicle accident per person in Europe each year (not including former Yugoslavia)[citation needed][when?]
10−4 2.4×10−4 Probability of being dealt a four of a kind in poker
10−3 Milli- (m) 1.3×10−3 Gaussian distribution: probability of a value being more than 3 standard deviations from the mean on a specific side[17]
1.4×10−3 Probability of a human birth giving triplets or higher-order multiples[18]
Probability of being dealt a full house in poker
1.9×10−3 Probability of being dealt a flush in poker
2.7×10−3 Probability of a random day of the year being your birthday (for all birthdays besides Feb. 29)
4×10−3 Probability of being dealt a straight in poker
10−2 Centi- (c) 1.8×10−2 Probability of winning any prize in the UK National Lottery with one ticket in 2003
2.1×10−2 Probability of being dealt a three of a kind in poker
2.3×10−2 Gaussian distribution: probability of a value being more than 2 standard deviations from the mean on a specific side[17]
2.7×10−2 Probability of winning any prize in the Powerball with one ticket in 2006
3.3×10−2 Probability of a human giving birth to twins[19]
4.8×10−2 Probability of being dealt a two pair in poker
10−1 Deci- (d) 1.6×10−1 Gaussian distribution: probability of a value being more than 1 standard deviation from the mean on a specific side[20]
1.7×10−1 Chance of rolling a '6' on a six-sided die
4.2×10−1 Probability of being dealt only one pair in poker
5.0×10−1 Chance of getting a 'head' in a coin toss. Physically less than 0.5; approximately 4.9983×10−1 for US nickel accounting for 1.67×10−4 (1-in-6000 chance) of coin landing on its edge.[21]
Probability of being dealt no pair in poker
100 1×100 Certain

References

  1. ↑ De Bianchi, Massimiliano Sassoli (2017-12-25), On the quantum "self-teleportation" probability of a human body, Brussels Free University, pp. 1–9, Bibcode: 2017arXiv171208465S 
  2. ↑ There are around 130,000 letters and 199,749 total characters in Hamlet; 26 letters ×2 for capitalization, 12 for punctuation characters = 64, 64199749 ≈ 10360,783.
  3. ↑ Kittel, Charles and Herbert Kroemer (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. pp. 53. ISBN 0-7167-1088-9. 
  4. ↑ Robert Matthews. "What are the odds of shuffling a deck of cards into the right order?". Science Focus. https://www.sciencefocus.com/science/what-are-the-odds-of-shuffling-a-deck-of-cards-into-the-right-order/. 
  5. ↑ Bridge hands
  6. ↑ "WD VelociRaptor Drive Specification Sheet (PDF)". 2012-04-13. http://www.wdc.com/wdproducts/library/SpecSheet/ENG/2879-701284.pdf. "With 1.4 million hours MTBF" 
  7. ↑ "NIST Radionuclide Half-Life Measurements". Nist. 2011-12-09. https://www.nist.gov/pml/data/halflife.cfm. Retrieved 2013-09-10. 
  8. ↑ "6 sigma". Wolfram Alpha. http://www.wolframalpha.com/input/?i=6+sigma&dataset=. "z>6 ... 9.866 x 10^-10" 
  9. ↑ "How to Play". Mega Millions. http://www.megamillions.com/how-to-play. "1 in 258,890,850" 
  10. ↑ Informed Sources Archive Alycidon Rail web site. Retrieved 29 April 2009. The site cites the source as an October 2000 article by Roger Ford in the magazine Modern Railways and based on a DETR survey.
  11. ↑ "5 sigma". http://www.wolframalpha.com/input/?i=5+sigma&dataset=. "z>5 ... 2.867 x 10^-7" 
  12. ↑ "Annual rates of lightning fatalities by country". Ronald L. Holle, Holle Meteorology & Photography – 2008. 2010-08-12. p. 7. http://www.vaisala.com/Vaisala%20Documents/Scientific%20papers/Annual_rates_of_lightning_fatalities_by_country.pdf. 
  13. ↑ Galindo, B. M.; Concepción, D.; Galindo, M. A.; Pérez, A.; Saiz, J. (2012). "Vaccine-related adverse events in Cuban children, 1999–2008.". MEDICC Review 14 (1): 38–43. doi:10.37757/MR2012V14.N1.8. PMID 22334111. http://www.medicc.org/mediccreview/index.php?issue=19&id=237&a=vahtml. 
  14. ↑ "Earth Impact Risk Summary: 2013 TV135 (Nov 7 arc=25 days)". archive.is: JPL. 2013-11-07. http://neo.jpl.nasa.gov/risk/2013tv135.html.  (5.9e-09 = 1 in 169,492,000 chance)
  15. ↑ "No, the Earth (Almost Certainly) Won't Get Hit by an Asteroid in 2032". Slate.com. 2013-10-18. http://www.slate.com/blogs/bad_astronomy/2013/10/18/asteroid_2013_tv135_bet_on_no_impact_from_this_rock.html. 
  16. ↑ "4 sigma". http://www.wolframalpha.com/input/?i=4+sigma&dataset=. "z>4 ... 3.167 x 10^-5" 
  17. ↑ 17.0 17.1 "Extreme Normal Probabilities". http://turner.faculty.swau.edu/mathematics/math241/materials/normalsigma/. "2.0 0.02275 ... 3.0 0.00134" 
  18. ↑ "Multiple Births". CDC. https://www.cdc.gov/nchs/fastats/multiple.htm. "Triplet or higher order birth rate: 137.0 per 100,000 live births" 
  19. ↑ "Multiple Births". CDC. https://www.cdc.gov/nchs/fastats/multiple.htm. "Twin birth rate: 33.2 per 1,000 live births" 
  20. ↑ "Introduction to Procedures Involving Sample Means". http://vassarstats.net/textbook/ch9pt1.html. "15.87% of all instances fall to the left of —1 standard deviation" 
  21. ↑ Murray, Daniel B.; Teare, Scott W. (1993-10-01). "Probability of a tossed coin landing on edge". Physical Review E 48 (4): 2547–2552. doi:10.1103/PhysRevE.48.2547. PMID 9960889. Bibcode: 1993PhRvE..48.2547M. 



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