Orders of magnitude (probability)

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This page is a progressive and labeled list of probability in orders of magnitude, with certain examples appended to some list objects.

List of orders of magnitude for probability
Factor SI prefix Value Item
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[1]
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[2]
10−68 1.0×10−68 Probability of shuffling a Standard 52-card deck in any specific order
10−28 4.47×10−28 Approximate probability of all four players in a game of bridge getting a complete suit[3]
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[4]
5.25×10−10 Caesium-137 Atom decay each second[5]
9.9×10−10 Gaussian distribution: probability of a value being more than 6 standard deviations from the mean on a specific side[6]
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*[7]
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
7.151×10−8 odds of winning the Jackpot (matching the 6 main numbers) in the UK National Lottery with one ticket in August 2009
10−7 1.17×10−7 Death per aircraft journey[8]
2.9×10−7 Gaussian distribution: probability of a value being more than 5 standard deviations from the mean on a specific side[9]
8.0×10−7 Death per person per year by lightning strike in Germany (Europe)[10]
10−6 Micro- (µ) 1×10−6 Life-threatening adverse reaction from a measles vaccine[11]
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 meter wide[12] will impact earth in 2032[13]
3.2×10−5 Gaussian distribution: probability of a value being more than 4 standard deviations from the mean on a specific side[14]
8.43×10−5 Probability of a deadly vehicle accident per person in Europe each year (not including Yugoslavia)
10−4 1×10−4 Asteroid 99942 Apophis impact in 2029 on earth
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[15]
1.4×10−3 Probability of a human birth giving triplets or higher-order multiples[16]
Probability of being dealt a full house in poker
1.9×10−3 Probability of being dealt a flush in poker
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[15]
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 birth giving twins[17]
4.8×10−2 Probability of being dealt a two pair in poker
10−1 Deci- (d) 1.04×10−1 Death per space shuttle journey[8]
1.6×10−1 Gaussian distribution: probability of a value being more than 1 standard deviation from the mean on a specific side[18]
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
Probability of being dealt no pair in poker
100 1×100 Almost sure

References[edit]

  1. ^ 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.
  2. ^ Kittel, Charles and Herbert Kroemer (1980). Thermal Physics (2nd ed.). W. H. Freeman Company. p. 53. ISBN 0-7167-1088-9. 
  3. ^ Bridge hands
  4. ^ "WD VelociRaptor Drive Specification Sheet (PDF)" (PDF). 2012-04-13. Retrieved 2013-11-22. With 1.4 million hours MTBF 
  5. ^ "NIST Radionuclide Half-Life Measurements". 2011-12-09. Retrieved 2013-09-10. 
  6. ^ "6 sigma". Wolfram Alpha. Retrieved 2013-12-07. z>6 ... 9.866 x 10^-10 
  7. ^ "How to Play". Mega Millions. Retrieved 2013-11-20. 1 in 258,890,850 
  8. ^ a b 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.
  9. ^ "5 sigma". Retrieved 2013-12-07. z>5 ... 2.867 x 10^-7 
  10. ^ "Annual rates of lightning fatalities by country" (PDF). Ronald L. Holle, Holle Meteorology & Photography - 2008. 2010-08-12. p. 7. Retrieved 2013-09-10. 
  11. ^ 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. PMID 22334111. 
  12. ^ "Earth Impact Risk Summary: 2013 TV135 (Nov 7 arc=25 days)". archive.is: JPL. 2013-11-07. Retrieved 2013-11-08.  (5.9e-09 = 1 in 169,492,000 chance)
  13. ^ "No, the Earth (Almost Certainly) Won't Get Hit by an Asteroid in 2032". Slate.com. 2013-10-18. Retrieved 2013-10-18. 
  14. ^ "4 sigma". Retrieved 2013-12-07. z>4 ... 3.167 x 10^-5 
  15. ^ a b "Extreme Normal Probabilities". Retrieved 2013-12-07. 2.0 0.02275 ... 3.0 0.00134 
  16. ^ "Multiple Births". CDC. Retrieved 2013-11-22. Triplet or higher order birth rate: 137.0 per 100,000 live births 
  17. ^ "Multiple Births". CDC. Retrieved 2013-11-22. Twin birth rate: 33.2 per 1,000 live births 
  18. ^ "Introduction to Procedures Involving Sample Means". Retrieved 2013-12-07. 15.87% of all instances fall to the left of —1 standard deviation