Orders of magnitude (probability)

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−$n\to \infty$	Almost never.
10−4.5×1029		10−4.5×1029	Probability of a human spontaneously teleporting 50 kilometres (31 miles) due to quantum effects
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
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
10−67		8.07×10−67	Probability of shuffling a standard 52-card deck in any specific order
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
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
		5.25×10−10	Caesium-137 atom decay each second
		9.9×10−10	Gaussian distribution: probability of a value being more than 6 standard deviations from the mean on a specific side
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*
		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
		2.9×10−7	Gaussian distribution: probability of a value being more than 5 standard deviations from the mean on a specific side
		8.0×10−7	Death per person per year by lightning strike in Germany (Europe)
10−6	Micro- (μ)	1×10−6	Life-threatening adverse reaction from a measles vaccine
		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 will impact earth in 2032
		3.2×10−5	Gaussian distribution: probability of a value being more than 4 standard deviations from the mean on a specific side
		8.43×10−5	Probability of a deadly vehicle accident per person in Europe each year (not including former Yugoslavia)
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
		1.4×10−3	Probability of a human birth giving triplets or higher-order multiples
			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
		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
		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
		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.
			Probability of being dealt no pair in poker
100		1×100	Certain