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sunrise problem wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 laplace s approach 2 see also 3 references 4 further reading toggle the table of contents sunrise problem 1 language العربية edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia problem asking the probability that the sun will rise tomorrow this article may contain original research please improve it by verifying the claims made and adding inline citations statements consisting only of original research should be removed june 2008 learn how and when to remove this message usually inferred from repeated observations the sun always rises in the east the sunrise problem can be expressed as follows what is the probability that the sun will rise tomorrow the sunrise problem illustrates the difficulty of using probability theory when evaluating the plausibility of statements or beliefs according to the bayesian interpretation of probability probability theory can be used to evaluate the plausibility of the statement the sun will rise tomorrow the sunrise problem was first introduced publicly in 1763 by richard price in his famous coverage of thomas bayes foundational work in bayesianism 1 laplace s approach edit pierre simon laplace approached the problem by means of his rule of succession 2 3 let p be the long run frequency of sunrises i e the sun rises on 100 p of days prior to knowing of any sunrises one is completely ignorant of the value of p laplace represented this prior ignorance by means of a uniform probability distribution on p for instance the probability that p is between 20 and 50 is just 30 this must not be interpreted to mean that in 30 of all cases p is between 20 and 50 rather it means that one s state of knowledge or ignorance justifies one in being 30 sure that the sun rises between 20 of the time and 50 of the time given the value of p and no other information relevant to the question of whether the sun will rise tomorrow the probability that the sun will rise tomorrow is p but we are not given the value of p what we are given is the observed data the sun has risen every day on record laplace inferred the number of days by saying that the universe was created about 6000 years ago based on a young earth creationist reading of the bible to find the conditional probability distribution of p given the data one uses bayes theorem which some call the bayes laplace rule having found the conditional probability distribution of p given the data one may then calculate the conditional probability given the data that the sun will rise tomorrow that conditional probability is given by the rule of succession the plausibility that the sun will rise tomorrow increases with the number of days on which the sun has risen so far specifically assuming p has an a priori distribution that is uniform over the interval 0 1 and that given the value of p the sun independently rises each day with probability p the desired conditional probability is pr sun rises tomorrow it has risen k times previously 0 1 p k 1 d p 0 1 p k d p k 1 k 2 displaystyle pr text sun rises tomorrow mid text it has risen k text times previously frac int _ 0 1 p k 1 dp int _ 0 1 p k dp frac k 1 k 2 by this formula if one has observed the sun rising 10000 times previously the probability it rises the next day is 10001 10002 0 99990002 displaystyle 10001 10002 approx 0 99990002 expressed as a percentage this is approximately a 99 990002 displaystyle 99 990002 chance however laplace recognized this to be a misapplication of the rule of succession through not taking into account all the prior information available immediately after deriving the result but this number the probability of the sun coming up tomorrow is far greater for him who seeing in the totality of phenomena the principle regulating the days and seasons realizes that nothing at present moment can arrest the course of it e t jaynes noted that laplace s warning had gone unheeded by workers in the field 4 a reference class problem arises the plausibility inferred will depend on whether we take the past experience of one person of humanity or of the earth a consequence is that each referent would hold different plausibility of the statement in bayesianism any probability is a conditional probability given what one knows that varies from one person to another see also edit rule of succession problem of induction doomsday argument a similar problem that raises intense philosophical debate newcomb s paradox unsolved problems in statistics additive smoothing also called laplace smoothing references edit bayes thomas 1763 12 31 lii an essay towards solving a problem in the doctrine of chances by the late rev mr bayes f r s communicated by mr price in a letter to john canton a m f r s philosophical transactions of the royal society of london in latin 53 53 409 410 doi 10 1098 rstl 1763 0053 issn 0261 0523 laplace pierre simon 1814 a philosophical essay on probabilities pdf translated by trruscott frederick wilson emory frederick lincoln john wiley son and chapman hall chung k l aitsahlia f 2003 elementary probability theory with stochastic processes and an introduction to mathematical finance springer pp 129 130 isbn 978 0 387 95578 0 jaynes e t 2003 chapter 18 6 in g larry bretthorst ed probability theory the logic of science cambridge university press p 564 doi 10 1017 cbo9780511790423 isbn 978 0 521 59271 0 archived from the original on 2022 06 03 further reading edit howie david 2002 interpreting probability controversies and developments in the early twentieth century cambridge university press pp 24 isbn 978 0 521 81251 1 v t e probability problems paradoxes bertrand s box paradox boy or girl paradox siegel s paradox sleeping beauty problem st petersburg paradox two envelopes problem classical puzzles balls into bins problem banach s matchbox problem birthday problem monty hall problem three prisoners problem urn problem waldegrave problem sampling and estimation coupon collector s problem german tank problem newton pepys problem moment problems hamburger moment problem hausdorff moment problem moment problem stieltjes moment problem trigonometric moment problem games and decision bertrand s ballot theorem gambler s ruin littlewood offord problem mabinogion sheep problem pill puzzle problem of points secretary problem sunrise problem geometric probability bertrand s paradox broken stick problem buffon s needle problem buffon s noodle mean line segment length sylvester s four point problem wendel s theorem category retrieved from https en wikipedia org w index php title sunrise_problem oldid 1356180723 categories probability problems statistical inference bayesian statistics hidden categories articles with short description short description matches wikidata articles that may contain original research from june 2008 all articles that may contain original research cs1 latin language sources la this page was last edited on 26 may 2026 at 04 43 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers 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