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 ValueItem
01.0×10−Almost never.
10−4.5×102910−4.5×1029Probability of a human spontaneously teleporting 50 kilometres (31 miles) due to quantum effects [1]
10−360,7831.0×10−360,783Probability of a monkey in front of a typewriter typing Hamlet on the first try, taking punctuation, capitalization and spacing into account [2]
10−183,8001.0×10−183,800Rough first estimate of the probability of a monkey in front of a typewriter typing all the letters of Hamlet on the first try [3]
10−678.07×10−67Probability of shuffling a standard 52-card deck in any specific order [4]
10−30 Quecto- (q)1×10−30One in 1,000,000,000,000,000,000,000,000,000,000
10−284.47×10−28Approximate probability of all four players in a game of bridge getting a complete suit [5]
10−27 Ronto- (r)1×10−27One in 1,000,000,000,000,000,000,000,000,000
10−24 Yocto- (y)1×10−24One in 1,000,000,000,000,000,000,000,000
10−21 Zepto- (z)1×10−21One in 1,000,000,000,000,000,000,000
10−192.83×10−19Approximate probability of matching 20 numbers for 20 in a game of keno
10−18 Atto- (a)1×10−18One in 1,000,000,000,000,000,000
10−162.74×10−16Probability of rolling snake eyes 10 times in a row on a pair of fair dice
10−15 Femto- (f)1×10−15One in 1,000,000,000,000,000
10−12 Pico- (p)1×10−12One in 1,000,000,000,000
10−112.52×10−11Approximate probability of one player in a game of bridge getting a complete suit
10−102.0×10−10Probability 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)1×10−9One in 1,000,000,000
3.9×10−9Probability of an entry winning the jackpot in the Mega Millions multi-state lottery in the United States* [9]
5.707×10−9Probability of winning the Grand Prize (matching all 6 numbers) in the US Powerball lottery with one ticket in January 2014
10−81.303×10−8Probability of winning the Grand Prize (matching all 6 numbers) in the Australian Powerball lottery with one ticket in March 2013
2.219×10−8odds of winning the Jackpot (matching the 6 main numbers from 59) in the UK National Lottery with one ticket since 10 October 2015
7.151×10−8odds of winning the Jackpot (matching the 6 main numbers from 49) in the UK National Lottery with one ticket until 10 October 2015
10−71.17×10−7Death 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]
8.0×10−7Death per person per year by lightning strike in Germany (Europe) [12]
10−6 Micro- (μ)1×10−6Life-threatening adverse reaction from a measles vaccine [13]
1.43×10−6Probability of the Yellowstone supervolcano erupting in a given year.
1.5×10−6Probability of being dealt a royal flush in poker
10−51.4×10−5Probability of being dealt a straight flush (other than a royal flush) in poker
1.6×10−5Risk 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]
8.43×10−5Probability of a deadly vehicle accident per person in Europe each year (not including former Yugoslavia)[ citation needed ][ when? ]
10−42.4×10−4Probability 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]
1.4×10−3Probability of a human birth giving triplets or higher-order multiples [18]
Probability of being dealt a full house in poker
1.9×10−3Probability of being dealt a flush in poker
2.7×10−3Probability of a random day of the year being your birthday (for all birthdays besides Feb. 29)
4×10−3Probability of being dealt a straight in poker
10−2 Centi- (c)1.8×10−2Probability of winning any prize in the UK National Lottery with one ticket in 2003
2.1×10−2Probability 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]
2.7×10−2Probability of winning any prize in the Powerball with one ticket in 2006
3.3×10−2Probability of a human giving birth to twins [19]
4.8×10−2Probability 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]
1.7×10−1Chance of rolling a '6' on a six-sided die
4.2×10−1Probability of being dealt only one pair in poker
5.0×10−1Chance 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
1001×100 Certain

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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, arXiv: 1712.08465 , 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. p. 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. Retrieved December 10, 2018.
  5. ↑ Bridge hands
  6. ↑ "WD VelociRaptor Drive Specification Sheet (PDF)" (PDF). 2012-04-13. Retrieved 2013-11-22. With 1.4 million hours MTBF
  7. ↑ "NIST Radionuclide Half-Life Measurements". Nist. 2011-12-09. Retrieved 2013-09-10.
  8. ↑ "6 sigma". Wolfram Alpha. Retrieved 2013-12-07. z>6 ... 9.866 x 10^-10
  9. ↑ "How to Play". Mega Millions. Retrieved 2013-11-20. 1 in 258,890,850
  10. ↑ Informed Sources Archive Archived 2014-05-22 at the Wayback Machine 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" . Retrieved 2013-12-07. z>5 ... 2.867 x 10^-7
  12. ↑ "Annual rates of lightning fatalities by country" (PDF). Ronald L. Holle, Holle Meteorology & Photography – 2008. 2010-08-12. p. 7. Retrieved 2013-09-10.
  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.
  14. ↑ "Earth Impact Risk Summary: 2013 TV135 (Nov 7 arc=25 days)". archive.is: JPL. 2013-11-07. Archived from the original on 2013-11-07. Retrieved 2013-11-08. (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. Retrieved 2013-10-18.
  16. ↑ "4 sigma" . Retrieved 2013-12-07. z>4 ... 3.167 x 10^-5
  17. 1 2 "Extreme Normal Probabilities" . Retrieved 2013-12-07. 2.0 0.02275 ... 3.0 0.00134
  18. ↑ "Multiple Births". CDC. Retrieved 2013-11-22. Triplet or higher order birth rate: 137.0 per 100,000 live births
  19. ↑ "Multiple Births". CDC. Retrieved 2013-11-22. Twin birth rate: 33.2 per 1,000 live births
  20. ↑ "Introduction to Procedures Involving Sample Means" . Retrieved 2013-12-07. 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. Bibcode:1993PhRvE..48.2547M. doi:10.1103/PhysRevE.48.2547. PMID   9960889.
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